A082940 -id:A082940 - cp's OEIS frontend

A082939 Numbers such that sum of the digits of the product of the factorial of digits of the number is equal to the sum of the digits of the number.

1, 2, 10, 18, 20, 22, 27, 36, 63, 72, 81, 100, 108, 114, 117, 126, 135, 141, 153, 162, 171, 180, 200, 202, 207, 216, 220, 261, 270, 306, 315, 333, 351, 360, 411, 513, 531, 603, 612, 621, 630, 702, 711, 720, 801, 810, 1000, 1008, 1014, 1017, 1026, 1035, 1041

Offset: 1

Meenakshi Srikanth (menakan_s(AT)yahoo.com), Apr 27 2003

			63 = 6!*3! = 720*6 = 4320, 4 + 3 + 2 + 0 = 9 and 6 + 3 = 9.

Suggested by Amarnath Murthy.

Michael S. Branicky, Table of n, a(n) for n = 1..10000

Cf. A007953, A066459, A082940.

from math import factorial, prod
def ok(n):
    d = list(map(int, str(n)))
    return sum(map(int, str(prod(map(factorial, d))))) == sum(d)
print([k for k in range(1042) if ok(k)]) # Michael S. Branicky, Aug 15 2022

Numbers k such that A007953(k) = A007953(A066459(k)).

Corrected and extended by Jason Earls, May 22 2004

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.

Original entry on oeis.org

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

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

Center digit is 9 from the third term onwards.

			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.

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

Cf. A082940.

Subsequence of A002113.

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 *)

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

cp's OEIS Frontend

A082939 Numbers such that sum of the digits of the product of the factorial of digits of the number is equal to the sum of the digits of the number.

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