A351328 a(n) is equal to the sum of the factorials of the digits of a(n-1), with a(1) = 0; each time a duplicated term appears, we replace it with the smallest integer not yet in the sequence and iterate.

0, 1, 2, 3, 6, 720, 5043, 151, 122, 5, 120, 4, 24, 26, 722, 5044, 169, 363601, 1454, 7, 5040, 146, 745, 5184, 40465, 889, 443520, 177, 10081, 40324, 57, 5160, 842, 40346, 775, 10200, 8, 40320, 34, 30, 9, 362880, 81369, 403927, 367953, 368772, 51128, 40444, 97, 367920, 368649, 404670, 5810, 40442, 75

Offset

1,3

Links

Carole Dubois, Table of n, a(n) for n = 1..10000

Michael De Vlieger, Scatterplot of a(n), n = 1..10^6.

Example

a(1) = 0; as 0! = 1 we have a(2) = 1; but as 1! = 1 is already in the sequence, we extend it with a(3) = 2, the smallest integer not yet in the sequence; as 2! = 2 (being already in the sequence) we extend it with a(4) = 3; now as 3! = 6 in new, we immediately form a(5) = 6; as 6! = 720 we have a(6) = 720 and a(7) = 7! + 2! + 0! = 5040 + 2 + 1 = 5043; etc.
This technique allows us to get rid of all the loops of the kind mentioned in A308259.

Mathematica

c[_] = 0; j = c[1] = 1; Array[Set[f[#], #!] &, 10, 0];
{1}~Join~Reap[Do[While[c[u] > 0, u++]; If[c[#] > 0, Set[k, u], Set[k, #]] &@ Total@ Map[f[#] &, IntegerDigits[j]]; Sow[k]; c[k] = i; j = k, {i, 2, 53}]][[-1, -1]] (* Michael De Vlieger, Feb 07 2022 *)

Crossrefs

Cf. A308259.

Sequence in context: A015762 A015770 A093038 * A367897 A094469 A015766

Adjacent sequences: A351325 A351326 A351327 * A351329 A351330 A351331

Keyword

base,nonn

Author

Eric Angelini and Carole Dubois, Feb 07 2022

Status

approved