A125832 -id:A125832 - cp's OEIS frontend

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

Giovanni Resta, Apr 02 2006

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

			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.

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

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

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 *)

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

A125834 Numbers that have exactly 15 representations as a product of two palindromes.

Original entry on oeis.org

4888884, 8896888, 13345332, 74732526, 100999899, 140732592, 179555376, 269130862, 295777482, 444888444, 734059326, 880968088, 978745768, 1032039008, 1183109928, 1321452132, 1399939992, 1548058512, 1614785172, 1886140256

Offset: 1

Farideh Firoozbakht, Dec 11 2006

			4888884 is in the sequence since 4888884 = 1*4888884 = 2*2444442 = 4*1222221 = 11*444444 = 22*222222 = 44*111111 = 111*44044 = 121*40404 = 222*22022 = 242*20202 = 444*11011 = 484*10101 = 1001*4884 = 1221*4004 = 2002*2442.

Cf. A002113, A116993, A125832, A125833, A125835.

f[n_]:=f[n]=Length[Select[Divisors[n],#<=n^(1/2)&&FromDigits[ Reverse[IntegerDigits[ # ]]]==#&&FromDigits[Reverse[IntegerDigits [n/# ]]]==n/#&]];Do[If[f[n]==15,Print[n]],{n,125000000}]

a(6)-a(20) from Donovan Johnson, Aug 05 2009

cp's OEIS Frontend

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

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