A219665 One more than the partial sums of A219661.

1, 2, 4, 9, 28, 111, 539, 3150, 21623, 172349, 1549897, 15401145, 168011253, 2003304294, 25928878273, 361788001016, 5411160126368, 86353882249912, 1464841397585336, 26323224850512720, 499551889319197566

Offset: 1

Author

Antti Karttunen, May 28 2013

Keywords

• nonn

Comments

Are there any cases after n>2, for which A219666(a(n)) = n! instead of n!+1 ? (At least for all terms a(3) - a(14) that number is n!+1.)

Compare to the conjecture given at A213710.

Crossrefs

One more than A226061.

Cf. A219652, A219666, A226061.

Cf. also A213710 (analogous sequence for base-2).

Programs

Mathematica

Accumulate@ Table[Length@ NestWhileList[# - Total@ IntegerDigits[#, MixedRadix[Reverse@ Range[2, 120]]] &, (n + 1)! - 1, # > n! - 1 &] - 1, {n, 0, 8}] + 1 (* Michael De Vlieger, Jun 27 2016, Version 10.2 *)

Scheme

(define (A219665 n) (+ 1 (A226061 n)))

Formula

a(n) = A226061(n)+1 = A219652(n!).

Extensions

Terms a(16) - a(21) computed from the new terms of A219661 by Antti Karttunen, Jun 27 2016