A082941 a(n) is the odd-length palindrome whose digits up to the center are those of n and whose center digit is equal to the digital root of the product of the factorial of n and the reverse of n.

111, 242, 393, 494, 595, 696, 797, 898, 999, 10901, 11911, 12921, 13931, 14941, 15951, 16961, 17971, 18981, 19991, 20902, 21912, 22922, 23932, 24942, 25952, 26962, 27972, 28982, 29992, 30903, 31913, 32923, 33933, 34943, 35953, 36963, 37973, 38983, 39993, 40904, 41914, 42924, 43934, 44944

Offset

1,1

Comments

Center digit is 9 from the third term onwards.

Links

J.W.L. (Jan) Eerland, Table of n, a(n) for n = 1..4999

Example

a(9) = 9!*9! = 362880*362880 = 131681894400. 1+3+1+6+8+1+8+9+4+4+0+0 = 45. 4+5 = 9.
a(6) = 6!*6! = 518400. 5+1+8+4+0+0 = 18. 1+8 = 9.

Mathematica

DeleteCases[ParallelTable[If[OddQ[Length[IntegerDigits[n]]]&&PalindromeQ[n]&&Part[IntegerDigits[n], Ceiling[(Length[IntegerDigits[n]])/2]]==FixedPoint[Total[IntegerDigits[#]]&, Factorial[Floor[n/10^Ceiling[Length[IntegerDigits[n]]/2]]]^2], n, a], {n, 100, 10^8}], a] (* J.W.L. (Jan) Eerland, Dec 26 2021 *)

Crossrefs

Cf. A082940.

Subsequence of A002113.

Sequence in context: A177769 A074842 A180115 * A029486 A097650 A271312

Adjacent sequences: A082938 A082939 A082940 * A082942 A082943 A082944

Keyword

nonn,base,less

Author

Meenakshi Srikanth (menakan_s(AT)yahoo.com), Apr 30 2003

Extensions

More terms from J.W.L. (Jan) Eerland, Dec 26 2021

Status

approved