A345405 Integers k such that k = (d1)_c + (d2)_c + ... + (dc)_c, where (d)_c denotes the descending factorial of d, c is the length of k and di is the i-th digit of k in base 10.
0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 36, 86, 15960
Offset: 1
Examples
(8)_2 + (6)_2 = 8*7 + 6*5 = 56 + 30 = 86, therefore 86 is in the list.
Programs
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Mathematica
q[n_] := Module[{dig = IntegerDigits[n], nd}, nd = Length[dig]; Sum[d!/(d - nd)!, {d, dig}] == n]; Select[Range[0, 16000], q] (* Amiram Eldar, Jun 18 2021 *)
Comments