A305231 Numbers that are the product of some integer and its digit reversal.

0, 1, 4, 9, 10, 16, 25, 36, 40, 49, 64, 81, 90, 100, 121, 160, 250, 252, 360, 400, 403, 484, 490, 574, 640, 736, 765, 810, 900, 976, 1000, 1008, 1089, 1207, 1210, 1300, 1458, 1462, 1600, 1612, 1729, 1855, 1936, 1944, 2268, 2296, 2430, 2500, 2520, 2668, 2701

Offset

1,3

Comments

Terms of A061205, sorted in increasing order, with duplicates removed.

Links

Jon E. Schoenfield, Table of n, a(n) for n = 1..10000 (first 1000 terms from Alois P. Heinz)

Example

12*21 = 252, so 252 is a term.
156*651 = 101556, so 101556 is a term. (It can also be written as 273*372; see A203924.)

Maple

a:= proc(n) option remember; local k, d; for k from 1+a(n-1) do
      for d in numtheory[divisors](k) do if k = d*(s-> parse(cat(
      seq(s[-i], i=1..length(s)))))(""||d) then return k fi od od
    end: a(1):=0:
seq(a(n), n=1..60);  # Alois P. Heinz, May 27 2018

Mathematica

a={0}; h=-1; For[k=0, k<=2701, k++, For[m=1, m<=DivisorSigma[0, k], m++, d=Divisors[k]; If[k/Part[d, m] == FromDigits[Reverse[IntegerDigits[Part[d, m]]]] && k>h , AppendTo[a, k]; h=k]]]; a (* Stefano Spezia, Jan 28 2023 *)

Prog

(PARI) isok(n) = if (n==0, return (1), fordiv(n, d, if (n/d == fromdigits(Vecrev(digits(d))), return (1))); return (0)); \\ Michel Marcus, May 28 2018

Crossrefs

Cf. A061205, A203924.

Cf. A325148 (squares), A359981 (nonsquares).

Sequence in context: A337816 A272266 A155566 * A312832 A236652 A236748

Adjacent sequences: A305228 A305229 A305230 * A305232 A305233 A305234

Keyword

nonn,base

Author

Jon E. Schoenfield, May 27 2018

Status

approved