cp's OEIS Frontend

This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.

Showing 1-3 of 3 results.

A085932 Numbers k such that (digits of k sorted in ascending order) + (digital sum of k) is a palindrome.

Original entry on oeis.org

1, 2, 3, 4, 10, 20, 30, 40, 100, 124, 129, 142, 148, 167, 176, 184, 192, 200, 214, 219, 224, 229, 241, 242, 248, 267, 276, 284, 291, 292, 300, 348, 367, 376, 384, 400, 412, 418, 421, 422, 428, 438, 448, 467, 476, 481, 482, 483, 484, 567, 576, 617, 627, 637
Offset: 1

Views

Author

Jason Earls and Amarnath Murthy, Jul 14 2003

Keywords

Comments

Essentially all terms can be generated by going over A009994. By permuting digits and including any number of 0's in any term that is in A009994 any term in this sequence can be found. For example, from 124 we find that 412, 1402, 200004001 are terms. - David A. Corneth, Apr 20 2024

Examples

			142 is a term because the digits of 142 in ascending order are 124, the digital sum of 124 is 7, and 124 + 7 = 131, a palindrome.

Links

Crossrefs

Cf. A009994, A085933, A085934, A085935.

Programs

  • Mathematica
    dspQ[n_]:=Module[{sidn=Sort[IntegerDigits[n]],pidn},pidn= IntegerDigits[ FromDigits[ sidn]+ Total[ sidn]]; pidn==Reverse[pidn]]; Select[Range[ 700], dspQ] (* Harvey P. Dale, Jul 19 2011 *)

A085934 Numbers k such that (digits of k sorted in ascending order) + (digital product of k) is a palindrome. Or, sortdigits(k) + digitproduct(k) is a palindrome.

Original entry on oeis.org

1, 2, 3, 4, 10, 16, 20, 28, 30, 39, 40, 50, 60, 61, 70, 80, 82, 89, 90, 93, 98, 100, 101, 110, 127, 166, 172, 179, 188, 197, 200, 202, 217, 220, 236, 247, 263, 271, 274, 300, 303, 326, 330, 348, 359, 362, 366, 384, 395, 400, 404, 427, 438, 440, 445, 454, 455, 472
Offset: 1

Views

Author

Jason Earls and Amarnath Murthy, Jul 14 2003

Keywords

Examples

			82 is a term because the digits of 82 sorted in ascending order are 28, the digital product of 82 is 16, and 28 + 16 = 44, a palindrome.

Links

Crossrefs

Cf. A085932, A085933, A085935.

Programs

  • Mathematica
    DeleteCases[ParallelTable[If[PalindromeQ[FromDigits[Sort[IntegerDigits[k]]]+Times@@IntegerDigits[k]],k,n],{k,1,10^7}],n] (* J.W.L. (Jan) Eerland, Nov 04 2024 *)

A085935 Palindromes in A085934.

Original entry on oeis.org

1, 2, 3, 4, 101, 202, 303, 404, 454, 505, 545, 606, 616, 636, 676, 707, 808, 818, 909, 1001, 2002, 3003, 4004, 5005, 6006, 7007, 8008, 9009, 10001, 10101, 11011, 20002, 20202, 22022, 22622, 30003, 30303, 33033, 34243, 40004, 40404, 43234, 44044
Offset: 1

Views

Author

Jason Earls and Amarnath Murthy, Jul 14 2003

Keywords

Examples

			616 is a member as the digits of 616 sorted in ascending order are 166 and the digital product of 166 is 36 and 166 + 36 = 202 is a palindrome.

Crossrefs

Cf. A085932, A085933, A085934.

Programs

  • Mathematica
    pdsQ[n_]:=Module[{ds=Sort[IntegerDigits[n]]},AllTrue[{n,FromDigits[ds]+ Times@@ds},PalindromeQ]]; Select[Range[45000],pdsQ] (* Requires Mathematica version 10 or later *) (* Harvey P. Dale, Jul 20 2020 *)
Showing 1-3 of 3 results.

Started in 1964 by Neil J. A. Sloane | Maintained by The OEIS Foundation Inc.

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