A334533 Numbers k such that k*sod(k) and k/sod(k) are both palindromes, where sod(k) denotes the sum of digits of k (A007953).

1, 2, 3, 42, 26664, 2640264, 26400264, 264000264, 2640000264, 26400000264, 264000000264, 2640000000264, 26400000000264, 144689999986441, 154698898896451, 226589999985622, 234779999977432, 243788999887342, 244788898887442, 253698898896352, 254689878986452

Offset

1,2

Comments

Intersection of A229549 and A334416.

264*(10^m+1) for m = 2 and m > 3 are terms. Among the first 1000 terms, most terms are palindromes or near-palindromes. The only terms where the first digit is not the same as the last digit among the first 1000 terms are: 42, 7458941369406538 and terms of the form 264*(10^m+1). - Chai Wah Wu, May 12 2020

Links

Chai Wah Wu, Table of n, a(n) for n = 1..10001 (n = 1..1000 from Giovanni Resta)

Example

The sum of digits of 26664 is 24 and 26664*24  = 639936 and 26664/24 = 1111 are palindromes, so 26664 is a term.

Mathematica

Select[Range[2.7*^6], (s = Plus @@ IntegerDigits[#]; Mod[#, s] == 0 && PalindromeQ[# s] && PalindromeQ[# /s]) &]

Prog

(PARI) ispal(k) = my(d=digits(k)); d==Vecrev(d);
isok(k) = my(s=sumdigits(k)); !(k%s) && ispal(k/s) && ispal(k*s); \\ Michel Marcus, May 05 2020

Crossrefs

Cf. A007953, A229549, A334416.

Sequence in context: A271331 A101821 A121475 * A196874 A087571 A126018

Adjacent sequences: A334530 A334531 A334532 * A334534 A334535 A334536

Keyword

nonn,base

Author

Giovanni Resta, May 05 2020

Status

approved