Permuted multiples: Difference between revisions

Line 378:

with javascript_semantics

atom t0 = time()

integer n = 3, n10 = 10, steps = 0

constant fmt="""

%s positive integer n for which (2..6)*n contain the same digits:

n = %,d (%,d steps, hmmm...)

2 x n = %,d

3 x n = %,d

4 x n = %,d

5 x n = %,d

6 x n = %,d

""",

limit = iff(platform()=JS?1e7:1e9)

string nowtelse = "Nothing", smother = "Smallest"

while true do

if n*6>=n10 then

printf(1,"~~Nothing~~ less than %,d (%,d steps)\n",{n10,steps})

printf(1,"%s less than %,d (%,d steps)\n",{nowtelse,n10,steps})

if n10>=limit then exit end if

n = n10+2

n10 *= 10

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if ins!=ns then exit end if

end for

if i=7 then~~ exit end if~~

if i=7 then

printf(1,fmt,{smother,n,steps} & sq_mul(n,tagset(6,2)))

nowtelse = "Nothing else"

smother = "Another"

exit -- (see below)

end if

n += 3

steps += 1

end if

end while

~~constant~~ ~~fmt~~="""

?elapsed(time()-t0)

Smallest positive integer n for which (2..6)*n contain the same digits:

n = %d

2 x n = %d

3 x n = %d

4 x n = %d

5 x n = %d

6 x n = %d

"""

printf(1,fmt,sq_mul(n,tagset(6)))

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Nothing less than 100,000 (2,222 steps)

Smallest positive integer n for which (2..6)*n contain the same digits:

n = ~~142857~~

n = 142,857 (14,285 steps, hmmm...)

2 x n = ~~285714~~

2 x n = 285,714

3 x n = ~~428571~~

3 x n = 428,571

4 x n = ~~571428~~

4 x n = 571,428

5 x n = ~~714285~~

5 x n = 714,285

6 x n = ~~857142~~

6 x n = 857,142

"0.1s"

</pre>

=== extended output ===

If we comment out that "exit -- (see below)", as per the AppleScript comments and the Pascal output,

some patterns start to emerge in the values and number of steps: *10 is a bit of a given, whereas

"insert 9s before the 8" is (for me) a bit more unexpected. Be warned: on the desktop, 1e8 takes

about 9s, 1e9 about 90s, so I'll predict 1e10 would take 15mins (and need 64bit) and I'll not try

to compete with Pascal in terms of performance, though I am getting very different results above 1e7.

Under pwa/p2js 1e8 takes about 30s (meh) so I've limited it to 1e7 (2.3s).

<pre>

Nothing else less than 1,000,000 (22,222 steps)

Another positive integer n for which (2..6)*n contain the same digits:

n = 1,428,570 (142,856 steps, hmmm...)

2 x n = 2,857,140

3 x n = 4,285,710

4 x n = 5,714,280

5 x n = 7,142,850

6 x n = 8,571,420

Another positive integer n for which (2..6)*n contain the same digits:

n = 1,429,857 (143,285 steps, hmmm...)

2 x n = 2,859,714

3 x n = 4,289,571

4 x n = 5,719,428

5 x n = 7,149,285

6 x n = 8,579,142

Nothing else less than 10,000,000 (222,222 steps)

Another positive integer n for which (2..6)*n contain the same digits:

n = 14,285,700 (1,428,566 steps, hmmm...)

2 x n = 28,571,400

3 x n = 42,857,100

4 x n = 57,142,800

5 x n = 71,428,500

6 x n = 85,714,200

Another positive integer n for which (2..6)*n contain the same digits:

n = 14,298,570 (1,432,856 steps, hmmm...)

2 x n = 28,597,140

3 x n = 42,895,710

4 x n = 57,194,280

5 x n = 71,492,850

6 x n = 85,791,420

Another positive integer n for which (2..6)*n contain the same digits:

n = 14,299,857 (1,433,285 steps, hmmm...)

2 x n = 28,599,714

3 x n = 42,899,571

4 x n = 57,199,428

5 x n = 71,499,285

6 x n = 85,799,142

Nothing else less than 100,000,000 (2,222,222 steps)

Another positive integer n for which (2..6)*n contain the same digits:

n = 142,857,000 (14,285,666 steps, hmmm...)

2 x n = 285,714,000

3 x n = 428,571,000

4 x n = 571,428,000

5 x n = 714,285,000

6 x n = 857,142,000

Another positive integer n for which (2..6)*n contain the same digits:

n = 142,985,700 (14,328,566 steps, hmmm...)

2 x n = 285,971,400

3 x n = 428,957,100

4 x n = 571,942,800

5 x n = 714,928,500

6 x n = 857,914,200

Another positive integer n for which (2..6)*n contain the same digits:

n = 142,998,570 (14,332,856 steps, hmmm...)

2 x n = 285,997,140

3 x n = 428,995,710

4 x n = 571,994,280

5 x n = 714,992,850

6 x n = 857,991,420

Another positive integer n for which (2..6)*n contain the same digits:

n = 142,999,857 (14,333,285 steps, hmmm...)

2 x n = 285,999,714

3 x n = 428,999,571

4 x n = 571,999,428

5 x n = 714,999,285

6 x n = 857,999,142

Nothing else less than 1,000,000,000 (22,222,222 steps)

</pre>