A219665 - OEIS

%I #22 Jun 29 2016 00:07:57

%S 1,2,4,9,28,111,539,3150,21623,172349,1549897,15401145,168011253,

%T 2003304294,25928878273,361788001016,5411160126368,86353882249912,

%U 1464841397585336,26323224850512720,499551889319197566

%N One more than the partial sums of A219661.

%C 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.)

%C Compare to the conjecture given at A213710.

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

%t 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 *)

%o (Scheme): (define (A219665 n) (+ 1 (A226061 n)))

%Y One more than A226061.

%Y Cf. A219652, A226061.

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

%K nonn

%O 1,2

%A _Antti Karttunen_, May 28 2013

%E Terms a(16) - a(21) computed from the new terms of A219661 by _Antti Karttunen_, Jun 27 2016