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

Author

Giovanni Resta, Apr 02 2006

Keywords

• nonn
• base

Comments

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

Examples

			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.
		

Links

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

Crossrefs

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

Programs

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 *)

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