A074889 Non-palindromic numbers such that the two largest proper divisors are palindromes having at least two digits and no other divisor is a palindrome with at least two digits.

524, 928, 1179, 1252, 1292, 1372, 1736, 2101, 2525, 2817, 4103, 4213, 4949, 8327, 8657, 8767, 10109, 10219, 19781, 23711, 25021, 27331, 28841, 34571, 41003, 41204, 45244, 45644, 46243, 47263, 48863, 49684, 50173, 52124, 53303, 53324, 56164, 56323, 56564, 56643

Offset

1,1

Links

David Consiglio, Jr., Table of n, a(n) for n = 1..212

David Consiglio, Jr., Python Program

Example

928 is here since the divisors of 928 are [1, 2, 4, 8, 16, 29, 32, 58, 116, *232*, *464*, 928].

Maple

ispali:= proc(n) local L;
  L:= convert(n, base, 10); evalb(L = ListTools:-Reverse(L))
end proc:
filter:= proc(n) local D;
  if ispali(n) then return false fi;
  D:= sort(convert(select(`>=`, numtheory:-divisors(n) minus {n}, 10), list));
  nops(D) >= 2 and select(ispali, D) = [D[-2], D[-1]];
end proc:
select(filter, [$1..10^5]); # Robert Israel, Oct 12 2015

Mathematica

tldp[n_]:=Module[{d=Select[Most[Divisors[n]], #>9&]}, Length[d]>1&&d[[-2]]> 9 && !PalindromeQ[n]&&AllTrue[Take[d, -2], PalindromeQ]&&NoneTrue[Drop[d, -2], PalindromeQ]]; Select[Range[57000], tldp] (* Requires Mathematica version 10 or later *) (* Harvey P. Dale, May 11 2021 *)

Crossrefs

Cf. A075407.

Sequence in context: A207356 A207199 A045209 * A249286 A283345 A125012

Adjacent sequences: A074886 A074887 A074888 * A074890 A074891 A074892

Keyword

base,nonn

Author

Jason Earls, Sep 13 2002

Extensions

Corrected and extended by David Consiglio, Jr., Oct 12 2015

Status

approved