# Palindromic gapful numbers ```perl constant @digits = '0','1','2','3','4','5','6','7','8','9'; # Infinite lazy iterator to generate palindromic "gap" numbers my @npal = flat [ @digits ], [ '00','11','22','33','44','55','66','77','88','99' ], { sink @^previous, @^penultimate; [ flat @digits.map: -> \digit { @penultimate.map: digit ~ * ~ digit } ] } … *; # Individual lazy palindromic gapful number iterators for each start/end digit my @gappal = (1..9).map: -> \digit { my \divisor = digit + 10 * digit; @npal.map: -> \this { next unless (my \test = digit ~ this ~ digit) %% divisor; test } } # Display ( "(Required) First 20 gapful palindromes:", ^20, 7 ,"\n(Required) 86th through 100th:", 85..99, 8 ,"\n(Optional) 991st through 1,000th:", 990..999, 10 ,"\n(Extra stretchy) 9,995th through 10,000th:", 9994..9999, 12 ,"\n(Meh) 100,000th:", 99999, 14 ).hyper(:1batch).map: -> $caption, $range, $fmt { my $now = now; say $caption; put "$_: " ~ @gappal[$_-1][|$range].fmt("%{$fmt}s") for 1..9; say round( now - $now, .001 ), " seconds"; } ``` #### Output: ``` (Required) First 20 gapful palindromes: 1: 121 1001 1111 1221 1331 1441 1551 1661 1771 1881 1991 10901 11011 12221 13431 14641 15851 17171 18381 19591 2: 242 2002 2112 2222 2332 2442 2552 2662 2772 2882 2992 20702 21912 22022 23232 24442 25652 26862 28182 29392 3: 363 3003 3333 3663 3993 31713 33033 36663 300003 303303 306603 309903 312213 315513 318813 321123 324423 327723 330033 333333 4: 484 4004 4224 4444 4664 4884 40304 42724 44044 46464 48884 400004 401104 402204 403304 404404 405504 406604 407704 408804 5: 5005 5115 5225 5335 5445 5555 5665 5775 5885 5995 50105 51315 52525 53735 54945 55055 56265 57475 58685 59895 6: 6006 6336 6666 6996 61116 64746 66066 69696 600006 603306 606606 609906 612216 615516 618816 621126 624426 627726 630036 633336 7: 7007 7777 77077 700007 707707 710017 717717 720027 727727 730037 737737 740047 747747 750057 757757 760067 767767 770077 777777 780087 8: 8008 8448 8888 80608 86768 88088 800008 802208 804408 806608 808808 821128 823328 825528 827728 829928 840048 842248 844448 846648 9: 9009 9999 94149 99099 900009 909909 918819 927729 936639 945549 954459 963369 972279 981189 990099 999999 9459549 9508059 9557559 9606069 0.111 seconds (Required) 86th through 100th: 1: 165561 166661 167761 168861 169961 170071 171171 172271 173371 174471 175571 176671 177771 178871 179971 2: 265562 266662 267762 268862 269962 270072 271172 272272 273372 274472 275572 276672 277772 278872 279972 3: 30366303 30399303 30422403 30455403 30488403 30511503 30544503 30577503 30600603 30633603 30666603 30699603 30722703 30755703 30788703 4: 4473744 4485844 4497944 4607064 4619164 4620264 4632364 4644464 4656564 4668664 4681864 4693964 4803084 4815184 4827284 5: 565565 566665 567765 568865 569965 570075 571175 572275 573375 574475 575575 576675 577775 578875 579975 6: 60399306 60422406 60455406 60488406 60511506 60544506 60577506 60600606 60633606 60666606 60699606 60722706 60755706 60788706 60811806 7: 72299227 72322327 72399327 72422427 72499427 72522527 72599527 72622627 72699627 72722727 72799727 72822827 72899827 72922927 72999927 8: 80611608 80622608 80633608 80644608 80655608 80666608 80677608 80688608 80699608 80800808 80811808 80822808 80833808 80844808 80855808 9: 95311359 95400459 95499459 95588559 95677659 95766759 95855859 95944959 96033069 96122169 96211269 96300369 96399369 96488469 96577569 0.046 seconds (Optional) 991st through 1,000th: 1: 17799771 17800871 17811871 17822871 17833871 17844871 17855871 17866871 17877871 17888871 2: 27799772 27800872 27811872 27822872 27833872 27844872 27855872 27866872 27877872 27888872 3: 3084004803 3084334803 3084664803 3084994803 3085225803 3085555803 3085885803 3086116803 3086446803 3086776803 4: 482282284 482414284 482535284 482656284 482777284 482898284 482909284 483020384 483141384 483262384 5: 57800875 57811875 57822875 57833875 57844875 57855875 57866875 57877875 57888875 57899875 6: 6084004806 6084334806 6084664806 6084994806 6085225806 6085555806 6085885806 6086116806 6086446806 6086776806 7: 7452992547 7453223547 7453993547 7454224547 7454994547 7455225547 7455995547 7456226547 7456996547 7457227547 8: 8085995808 8086006808 8086116808 8086226808 8086336808 8086446808 8086556808 8086666808 8086776808 8086886808 9: 9675005769 9675995769 9676886769 9677777769 9678668769 9679559769 9680440869 9681331869 9682222869 9683113869 0.282 seconds (Extra stretchy) 9,995th through 10,000th: 1: 1787447871 1787557871 1787667871 1787777871 1787887871 1787997871 2: 2787447872 2787557872 2787667872 2787777872 2787887872 2787997872 3: 308757757803 308760067803 308763367803 308766667803 308769967803 308772277803 4: 48326662384 48327872384 48329192384 48330303384 48331513384 48332723384 5: 5787447875 5787557875 5787667875 5787777875 5787887875 5787997875 6: 608760067806 608763367806 608766667806 608769967806 608772277806 608775577806 7: 746951159647 746958859647 746961169647 746968869647 746971179647 746978879647 8: 808690096808 808691196808 808692296808 808693396808 808694496808 808695596808 9: 968688886869 968697796869 968706607869 968715517869 968724427869 968733337869 3.114 seconds (Meh) 100,000th: 1: 178788887871 2: 278788887872 3: 30878611687803 4: 4833326233384 5: 578789987875 6: 60878611687806 7: 74826144162847 8: 80869688696808 9: 96878077087869 32.603 seconds ``` --- # Agent Instructions: Querying This Documentation If you need additional information that is not directly available in this page, you can query the documentation dynamically by asking a question. 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