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
Examples
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.
Links
- J.W.L. (Jan) Eerland, Table of n, a(n) for n = 1..4999
Programs
-
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 *)
Extensions
More terms from J.W.L. (Jan) Eerland, Dec 26 2021
Comments