Strange numbers
n is a strange number if every adjacent decimal digit differs from its neighbour by a prime number.
Where 100 < n < 500
- Stretch goal
Show the number of 10-digit strange numbers that begin with 1
ALGOL W
<lang algolw>begin % find "strange numbers" - numbers where digits differ from the next %
% by a prime %
% returns true if n is strange, false otherwise %
logical procedure isStrange( integer value n ) ;
begin
integer rest;
rest := abs( n );
if rest < 10 then false
else begin
logical strange;
integer d0;
strange := true;
d0 := rest rem 10;
rest := rest div 10;
while strange and rest > 0 do begin
integer d1, diff;
d1 := rest rem 10;
rest := rest div 10;
diff := abs( d1 - d0 );
strange := diff = 2 or diff = 3 or diff = 5 or diff = 7;
d0 := d1
end while_strange_and_rest_gt_0 ;
strange
end if_rest_lt_10__
end isStrange ;
% test the isStrange procedure on values 100-499 %
begin
integer strangeCount;
strangeCount := 0;
for n := 100 until 499 do begin;
if isStrange( n ) then begin
strangeCount := strangeCount + 1;
if strangeCount rem 20 = 1
then write( i_w := 4, s_w := 0, n )
else writeon( i_w := 4, s_w := 0, n )
end if_isStrange_n
end for_n
end
end.</lang>
- Output:
130 131 135 136 138 141 142 146 147 149 161 163 164 168 169 181 183 185 186 202 203 205 207 241 242 246 247 249 250 252 253 257 258 270 272 274 275 279 292 294 296 297 302 303 305 307 313 314 316 318 350 352 353 357 358 361 363 364 368 369 381 383 385 386 413 414 416 418 420 424 425 427 429 461 463 464 468 469 470 472 474 475 479 492 494 496 497
Factor
<lang factor>USING: grouping io kernel math.ranges math.statistics math.text.utils math.vectors prettyprint sequences ;
- strange? ( n -- ? )
1 digit-groups differences vabs
[ { 2 3 5 7 } member? ] all? ;
"Strange numbers in (100, 500):" print nl 100 500 (a,b) [ strange? ] filter dup 10 group [ [ pprint bl ] each nl ] each nl length pprint " strange numbers found." print</lang>
- Output:
Strange numbers in (100, 500): 130 131 135 136 138 141 142 146 147 149 161 163 164 168 169 181 183 185 186 202 203 205 207 241 242 246 247 249 250 252 253 257 258 270 272 274 275 279 292 294 296 297 302 303 305 307 313 314 316 318 350 352 353 357 358 361 363 364 368 369 381 383 385 386 413 414 416 418 420 424 425 427 429 461 463 464 468 469 470 472 474 475 479 492 494 496 497 87 strange numbers found.
Pascal
simple brute force, by adding a prime difference from digit to digit. <lang pascal>program strangenumbers; type
tDeltaIdx = 0..7;
const
dgtCnt = 3; deltaprime : array[tDeltaIdx] of Int32 =(-7,-5,-3,-2,2,3,5,7);
//globals are set to 0 var
Digits : array[0..dgtCnt-1] of Int32; Actdgt,i,j,k,Cnt : Int32;
procedure OutPut; Begin
write(Digits[0],Digits[1],Digits[2],' ');
end;
Begin
For i := 1 to 4 do
Begin
Digits[0] := i;
For k in tDeltaIdx do
Begin
if (i+deltaprime[k]) in [0..9] then
Begin
Actdgt := i+deltaprime[k];
Digits[1]:= Actdgt;
For j in tDeltaIdx do
if (Actdgt+deltaprime[j]) in [0..9] then
Begin
Digits[2]:= Actdgt+deltaprime[j];
OutPut;
inc(cnt);
If cnt MOD 20 = 0 then
writeln;
end;
end;
end;
end;
writeln;
Writeln('Count : ',cnt);
end. </lang>
- Output:
130 131 135 136 138 141 142 146 147 149 161 163 164 168 169 181 183 185 186 202 203 205 207 241 242 246 247 249 250 252 253 257 258 270 272 274 275 279 292 294 296 297 302 303 305 307 313 314 316 318 350 352 353 357 358 361 363 364 368 369 381 383 385 386 413 414 416 418 420 424 425 427 429 461 463 464 468 469 470 472 474 475 479 492 494 496 497 Count : 87
Phix
<lang Phix>function strange(integer left, sequence digits, res={}, part={})
for i=1 to length(digits) do
integer di = digits[i]
if left=1 then
string fmt = join(repeat("%d",length(part)+1),"")
res = append(res,sprintf(fmt,part&di))
else
sequence nxt = filter(sq_add(di,{-7,-5,-3,-2,2,3,5,7}),"in",{0,9},"[]")
res = strange(left-1,nxt,res,part&di)
end if
end for
return res
end function sequence res = strange(3,tagset(4)) -- (3 digit numbers beginning 1..4) printf(1,"%d strange numbers found: %v\n",{length(res),shorten(res,"",5)})</lang>
- Output:
87 strange numbers found: {"130","131","135","136","138","...","479","492","494","496","497"}
stretch goal
<lang Phix>res = strange(10,tagset(1)) printf(1,"%,d 10-digit strange numbers beginning with 1: %v (%s)\n",
{length(res),shorten(res,"",2),elapsed(time())})</lang>
- Output:
853,423 10-digit strange numbers beginning with 1: {"1302020202","1302020203","...","1869797975","1869797979"} (4.8s)
Raku
<lang perl6># 20210222 Raku programming solution
sub infix:<′>(\x,\y) { abs(x -y) ∈ [2, 3, 5, 7] ?? True !! False }
for (101..499) { .say if so all .comb.rotor(2 => -1).map: { @_[0] ′ @_[1] } }</lang>
- Output:
./strange.raku | wc 87 87 348
REXX
<lang rexx>/*REXX pgm lists a bunch of strange numbers, integers whose digits differ by a prime. */ parse arg LO HI . /*obtain optional arguments from the CL*/ if LO== | LO=="," then LO= 100 + 1 /*Not specified? Then use the default.*/ if HI== | HI=="," then HI= 500 - 1 /* " " " " " " */ !.= 0; !.2= 1; !.3= 1; !.5= 1; !.7= 1 /*build a list of digits that are prime*/ $= /*the list of strange numbers (so far).*/
do j=LO to HI; L= length(j) /*find for strange numbers in the range*/
if L==1 then iterate /*Number too short? Then skip it. */
do k=1 for L-1 /*examine the difference in the digits.*/
dif= abs( substr(j, k, 1) - substr(j, k + 1, 1) ) /* │difference│ */
if \!.dif then iterate j /*Difference not prime? Then skip it. */
end /*k*/
$= $ j /*add the number to the "strange" list.*/
end /*j*/
/*stick a fork in it, we're all done. */
say words($) ' strange numbers found between ' LO " and " HI ' (inclusive):'; say say strip($)</lang>
- output when using the default inputs:
87 strange numbers found between 101 and 499 (inclusive): 130 131 135 136 138 141 142 146 147 149 161 163 164 168 169 181 183 185 186 202 203 205 207 241 242 246 247 249 250 252 253 257 258 270 272 274 275 279 292 294 296 297 302 303 305 307 313 314 316 318 350 352 353 357 358 361 363 364 368 369 381 383 385 386 413 414 416 418 420 424 425 427 429 461 463 464 468 469 470 472 474 475 479 492 494 496 497
Ring
<lang ring> load "stdlib.ring"
row = 0 see "Strange numbers are:"
for n = 100 to 500
flag = 1
str = string(n)
for m = 1 to len(str)-1
num1 = number(str[m])
num2 = number(str[m+1])
pr = fabs(num1-num2)
if not isprime(pr)
flag = 0
exit
ok
next
if flag = 1
row = row + 1
if (row-1) % 11 = 0
see nl
else
see " " + str
ok
ok
next </lang>
- Output:
Strange numbers are: 131 135 136 138 141 142 146 147 149 161 164 168 169 181 183 185 186 202 203 205 241 242 246 247 249 250 252 253 257 258 272 274 275 279 292 294 296 297 302 303 307 313 314 316 318 350 352 353 357 358 363 364 368 369 381 383 385 386 413 414 418 420 424 425 427 429 461 463 464 468 470 472 474 475 479 492 494 496 497
Wren
<lang ecmascript>var primes = [2, 3, 5, 7] var count = 0 var d = [] System.print("Strange numbers in the open interval (100, 500) are:\n") for (i in 101..499) {
d.clear()
var j = i
while (j > 0) {
d.add(j % 10)
j = (j/10).floor
}
if (primes.contains((d[0] - d[1]).abs) && primes.contains((d[1] - d[2]).abs)) {
System.write("%(i) ")
count = count + 1
if (count % 10 == 0) System.print()
}
} if (count % 10 != 0) System.print() System.print("\n%(count) strange numbers in all.")</lang>
- Output:
Strange numbers in the open interval (100, 500) are: 130 131 135 136 138 141 142 146 147 149 161 163 164 168 169 181 183 185 186 202 203 205 207 241 242 246 247 249 250 252 253 257 258 270 272 274 275 279 292 294 296 297 302 303 305 307 313 314 316 318 350 352 353 357 358 361 363 364 368 369 381 383 385 386 413 414 416 418 420 424 425 427 429 461 463 464 468 469 470 472 474 475 479 492 494 496 497 87 strange numbers in all.