A244090 Numbers n such that n is a factorion (A014080, equal to the sum of the factorials of its digits), in at least one base b.

1, 2, 7, 25, 26, 48, 49, 121, 122, 144, 145, 240, 721, 722, 726, 1440, 1441, 1442, 5041, 5042, 5162, 5760

Offset

1,2

Comments

The bases in which n = func(n) are 2, 2, 4, 6, 6, 11, 5, 24, 24, 28, 10, 47, 120, 120, 240, 239, 15, 15, 720, 720, 27, 822. Note multiple bases for some n, e.g. 25 = 4! + 1! in base 6 and 25 = 1! + 4! in base 21; 721 = 6! + 1! in base 120 and 721 = 1! + 6! in base 715.

Links

Table of n, a(n) for n=1..22.

Wikipedia, Factorion

Formula

s = 0; for digit(i=1..j) of n in base b, s = s + digit(i)!.

Example

1 = 1! = 1 (base>=2).
2 = 1! + 0! = 1 + 1 = 10 (b=2).
7 = 1! + 3! = 1 + 6 = 13 (b=4).
25 = 4! + 1! = 24 + 1 = 41 (b=6).
26 = 4! + 2! = 24 + 2 = 42 (b=6).
48 = 4! + 4! = 24 + 24 = 44 (b=11).
49 = 1! + 4! + 4! = 1 + 24 + 24 = 144 (b=5).
121 = 5! + 1! = 120 + 1 = 51 (b=24).
122 = 5! + 2! = 120 + 2 = 52 (b=24).
144 = 5! + 4! = 120 + 24 = 54 (b=28).
145 = 1! + 4! + 5! = 1 + 24 + 120 (b=10).
240 = 5! + 5! = 120 + 120 = 55 (b=47).

Prog

(PARI) isok(n) = {if (n==1, return (1)); for (b=2, n, d = digits(n, b); if (sum(i=1, #d, d[i]!) == n, return (1)); ); return (0); } \\ Michel Marcus, Jun 21 2014

Crossrefs

Cf. A193163, A014080.

Sequence in context: A236422 A013204 A013209 * A247880 A330051 A145130

Adjacent sequences: A244087 A244088 A244089 * A244091 A244092 A244093

Keyword

nonn,base,more

Author

Anthony Sand, Jun 20 2014

Status

approved