A116993 a(n) is the least number having exactly n representations as a product of two palindromes.

13, 1, 4, 44, 66, 484, 4444, 7326, 6666, 48884, 73326, 493284, 888888, 666666, 5426124, 4888884, 6672666, 7333326, 44888844, 73399326, 246888642, 67333266, 4073662593, 4893772884, 4533773244, 6800659866, 2715775062, 1481331852, 493777284, 740665926, 8147325186, 5431550124, 74807258526

Offset

0,1

Comments

a(20) <= 733333326; a(34) <= 666666666666; a(39) <= 4888888888884 and a(44) <= 7333333333326. - Farideh Firoozbakht, Dec 10 2006

Links

Table of n, a(n) for n=0..32.

David A. Corneth, Some upper bounds on a(n)

Example

a(0)=13 since 13 is the smallest number that cannot be represented as a product of two palindromes.
a(5)=484 since 484 = 1*484 = 2*242 = 4*121 = 22*22 = 11*44.

Mathematica

f[n_]:=f[n]=Length[Select[Divisors[n], #<=n^(1/2)&&FromDigits[ Reverse[IntegerDigits[ # ]]]==#&&FromDigits[Reverse[IntegerDigits [n/# ]]]==n/#&]]; a[n_]:=(For[m=1, f[m] != n, m++ ]; m); Do[Print[a[n]], {n, 0, 18}] (* Farideh Firoozbakht, Dec 10 2006 *)

Crossrefs

Cf. A002113, A125832, A125833, A125834, A140332.

Sequence in context: A010232 A010233 A159820 * A010234 A111738 A389368

Adjacent sequences: A116990 A116991 A116992 * A116994 A116995 A116996

Keyword

nonn,base

Author

Giovanni Resta, Apr 02 2006

Extensions

More terms from Farideh Firoozbakht, Dec 10 2006

a(19)-a(27) from Donovan Johnson, Aug 04 2009

More terms from David A. Corneth, Aug 10 2025

Status

approved