A165163 Sequence is obtained from Catalan numbers (A000108) by taking the factorial of each digit and adding them up.

1, 1, 2, 120, 25, 26, 9, 362906, 32, 41066, 369361, 86520, 40327, 367948, 5835, 766968, 11053, 731572, 56192, 374411, 1615, 7256, 404818, 364605, 771205, 404861, 51385, 727600, 379721, 42643, 807308, 1091011, 495081, 807, 777014, 772751, 1578665, 410061, 108045

Offset

0,3

Comments

The primes in this sequence are 2, 369361, 379721, 42643, 1008859, 1505873, 2388293, 3289723, .... [Extended by Robert G. Wilson v, Sep 30 2009]

Links

Table of n, a(n) for n=0..38.

Dario Alpern, Factorization using the Elliptic Curve Method

Formula

a(n) = A061602(A000108(n)). - Alois P. Heinz, Jul 09 2023

Example

The sum of the factorials of each digit of 9694845 = 9! + 6! + 9! + 4! + 8! + 4! + 5! = 766968.

Maple

a:= n-> add(i!, i=convert(binomial(2*n, n)/(n+1), base, 10)):
seq(a(n), n=0..42);  # Alois P. Heinz, Jul 09 2023

Mathematica

f[n_] := Plus @@ (IntegerDigits@ n!); Table[f@ CatalanNumber@ n, {n, 0, 35}] (* Robert G. Wilson v, Sep 30 2009 *)

Crossrefs

Cf. A000108, A061602.

Sequence in context: A024030 A221231 A243512 * A153658 A073785 A102355

Adjacent sequences: A165160 A165161 A165162 * A165164 A165165 A165166

Keyword

nonn,base

Author

Parthasarathy Nambi, Sep 06 2009

Extensions

a(16) onwards added and offset changed from 1 to 0 by Robert G. Wilson v, Sep 30 2009

Status

approved