A082941 - OEIS

%I #25 Feb 12 2022 13:45:56

%S 111,242,393,494,595,696,797,898,999,10901,11911,12921,13931,14941,

%T 15951,16961,17971,18981,19991,20902,21912,22922,23932,24942,25952,

%U 26962,27972,28982,29992,30903,31913,32923,33933,34943,35953,36963,37973,38983,39993,40904,41914,42924,43934,44944

%N 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.

%C Center digit is 9 from the third term onwards.

%H J.W.L. (Jan) Eerland, <a href="/A082941/b082941.txt">Table of n, a(n) for n = 1..4999</a>

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

%e a(6) = 6!*6! = 518400. 5+1+8+4+0+0 = 18. 1+8 = 9.

%t 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 *)

%Y Cf. A082940.

%Y Subsequence of A002113.

%K nonn,base,less

%O 1,1

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

%E More terms from _J.W.L. (Jan) Eerland_, Dec 26 2021