A334533 - OEIS

%I #24 May 18 2020 22:40:24

%S 1,2,3,42,26664,2640264,26400264,264000264,2640000264,26400000264,

%T 264000000264,2640000000264,26400000000264,144689999986441,

%U 154698898896451,226589999985622,234779999977432,243788999887342,244788898887442,253698898896352,254689878986452

%N 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).

%C Intersection of A229549 and A334416.

%C 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

%H Chai Wah Wu, <a href="/A334533/b334533.txt">Table of n, a(n) for n = 1..10001</a> (n = 1..1000 from Giovanni Resta)

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

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

%o (PARI) ispal(k) = my(d=digits(k)); d==Vecrev(d);

%o isok(k) = my(s=sumdigits(k)); !(k%s) && ispal(k/s) && ispal(k*s); \\ _Michel Marcus_, May 05 2020

%Y Cf. A007953, A229549, A334416.

%K nonn,base

%O 1,2

%A _Giovanni Resta_, May 05 2020