Cyclops numbers
Template:Draft A cyclops number is a number with an odd number of digits that has a zero in the center, but nowhere else. They are named so in tribute to the one eyed giants Cyclops from Greek mythology.
Cyclops numbers can be found in any base. This task strictly is looking for cyclops numbers in base 10.
There are many different classifications of cyclops numbers with minor differences in characteristics. In an effort to head off a whole series of tasks with tiny variations, we will cover several variants here.
- Task
- Find and display here on this page the first 50 cyclops numbers in base 10 (all of the sub tasks are restricted to base 10).
- Find and display here on this page the first 50 prime cyclops numbers. (cyclops numbers that are prime.)
- Find and display here on this page the first 50 blind prime cyclops numbers. (prime cyclops numbers that remain prime when "blinded"; the zero is removed from the center.)
- Find and display here on this page the first 50 palindromic prime cyclops numbers. (prime cyclops numbers that are palindromes.)
- Stretch
- Find and display the first cyclops number greater than one million (1,000,000) and the index (place) in the series where it is found.
- Find and display the first prime cyclops number greater than one million (1,000,000) and the index (place) in the series where it is found.
- Find and display the first blind prime cyclops number greater than one million (1,000,000) and the index (place) in the series where it is found.
- Find and display the first palindromic prime cyclops number greater than one million (1,000,000) and the index (place) in the series where it is found.
- See also
Raku
<lang perl6>my @cyclops = lazy gather for 0..* -> $exp {
(exp($exp, 10) ..^ exp($exp + 1, 10)).map: -> $start {
next if $start.contains: 0;
for exp($exp, 10) ..^ exp($exp + 1, 10) -> $end {
next if $end.contains: 0;
take $start ~ 0 ~ $end;
}
}
}
my @prime-cyclops = @cyclops.grep: { .is-prime };
my @blind-cyclops = @prime-cyclops.grep: { .trans('0' => ).is-prime };
my @palindrome-cyclops = @prime-cyclops.grep: { $_ eq .flip };
for , @cyclops,
'prime ', @prime-cyclops,
'blind prime ', @blind-cyclops,
'palindromic prime ', @palindrome-cyclops
-> $type, $iterator {
say "\n\nFirst 50 {$type}cyclops numbers:\n" ~ $iterator[^50].batch(10)».fmt("%7d").join("\n") ~
"\n\nFirst {$type}cyclops number > 1,000,000: " ~ $iterator.first( * > 1e7 ) ~
" - at (zero based) index: " ~ $iterator.first: * > 1e7, :k;
}</lang>
- Output:
First 50 cyclops numbers:
101 102 103 104 105 106 107 108 109 201
202 203 204 205 206 207 208 209 301 302
303 304 305 306 307 308 309 401 402 403
404 405 406 407 408 409 501 502 503 504
505 506 507 508 509 601 602 603 604 605
First cyclops number > 1,000,000: 111101111 - at (zero based) index: 538083
First 50 prime cyclops numbers:
101 103 107 109 307 401 409 503 509 601
607 701 709 809 907 11027 11047 11057 11059 11069
11071 11083 11087 11093 12011 12037 12041 12043 12049 12071
12073 12097 13033 13037 13043 13049 13063 13093 13099 14011
14029 14033 14051 14057 14071 14081 14083 14087 15013 15017
First prime cyclops number > 1,000,000: 111101129 - at (zero based) index: 39319
First 50 blind prime cyclops numbers:
101 103 107 109 307 401 503 509 601 607
701 709 809 907 11071 11087 11093 12037 12049 12097
13099 14029 14033 14051 14071 14081 14083 14087 15031 15053
15083 16057 16063 16067 16069 16097 17021 17033 17041 17047
17053 17077 18047 18061 18077 18089 19013 19031 19051 19073
First blind prime cyclops number > 1,000,000: 111101161 - at (zero based) index: 11393
First 50 palindromic prime cyclops numbers:
101 16061 31013 35053 38083 73037 74047 91019 94049 1120211
1150511 1160611 1180811 1190911 1250521 1280821 1360631 1390931 1490941 1520251
1550551 1580851 1630361 1640461 1660661 1670761 1730371 1820281 1880881 1930391
1970791 3140413 3160613 3260623 3310133 3380833 3460643 3470743 3590953 3670763
3680863 3970793 7190917 7250527 7310137 7540457 7630367 7690967 7750577 7820287
First palindromic prime cyclops number > 1,000,000: 114808411 - at (zero based) index: 66