A085935 -id:A085935 - cp's OEIS frontend

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

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

Jason Earls and Amarnath Murthy, Jul 14 2003

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

			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.

David A. Corneth, Table of n, a(n) for n = 1..10000

Cf. A009994, A085933, A085934, A085935.

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

Jason Earls and Amarnath Murthy, Jul 14 2003

			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.

J.W.L. (Jan) Eerland, Table of n, a(n) for n = 1..4284 (all terms <= 10000000)

Cf. A085932, A085933, A085935.

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 *)

A085933 Palindromes in A085932.

Original entry on oeis.org

1, 2, 3, 4, 242, 292, 484, 676, 18581, 20402, 20902, 40804, 60706, 81518, 1085801, 1805081, 2004002, 2009002, 4008004, 6007006, 8015108, 8105018, 100858001, 108050801, 180050081, 200040002, 200090002, 400080004, 600070006, 800151008, 801050108, 810050018

Offset: 1

Jason Earls and Amarnath Murthy, Jul 14 2003

Sequence is infinite since there is no restriction on the number of zeros.

This sequence is the union of {1, 2, 3, 4}, {2*100^k + 4*10^k + 2}, {2*100^k + 9*10^k + 2}, {4*100^k + 8*10^k + 4}, {6*100^k + 7*10^k + 6}, {100^(k+1) + 8*10^(2*k-m+2) + 5*10^(k+1) + 8*10^m + 1} and {8*100^(k+1) + 10^(2*k-m+2) + 5*10^(k+1) + 10^m + 8}, where k >= 1 and 1 <= m <= k. - Jinyuan Wang, Mar 24 2020

			242 is a member because 229 + (2 + 2 + 9) = 242.

Cf. A085932, A085934, A085935.

Example corrected by Harvey P. Dale, Sep 08 2018

More terms from Jinyuan Wang, Mar 24 2020

cp's OEIS Frontend

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

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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.

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A085933 Palindromes in A085932.

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