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

Author

Andrzej Kukla, Jun 18 2021

Keywords

• nonn
• fini
• full
• base

Comments

The descending factorial (d)_c is defined as d*(d-1)*(d-2)*...*(d-c+1).

Examples

			(8)_2 + (6)_2 = 8*7 + 6*5 = 56 + 30 = 86, therefore 86 is in the list.
		

Crossrefs

Cf. A014080 (factorions), A068424 (descending factorials), A345406.

Programs

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 *)