A131841 Additive persistence of Woodall numbers.

0, 0, 1, 1, 2, 2, 2, 2, 2, 2, 2, 2, 2, 3, 3, 2, 2, 2, 3, 2, 2, 2, 2, 2, 3, 2, 2, 2, 2, 3, 2, 3, 3, 3, 3, 2, 3, 2, 2, 2, 3, 3, 3, 3, 3, 2, 2, 3, 3, 3, 3, 3, 3, 2, 3, 2, 3, 2, 3, 3, 3, 3, 3, 3, 3, 2, 2, 3, 2, 2, 3, 3, 3, 2, 2, 2, 2, 2, 3, 2, 2, 2, 3, 3, 2, 3, 3, 3

Offset

1,5

Links

Table of n, a(n) for n=1..88.

Formula

a(n) = A031286(A003261(n)). - James C. McMahon, Mar 01 2025

Example

Woodall number 159 --> 1+5+9=15 --> 1+5=6 thus persistence is 2

Maple

with(numtheory): with(combinat): P:=proc(n) local a, t; t:=0; a:=n*2^n-1; while a>9 do t:=t+1; a:=convert(convert(a, base, 10), `+`); od; t;
end: seq(P(i), i=1..10^2);

Mathematica

f[n_] := Length@ NestWhileList[Plus @@ IntegerDigits@# &, n*2^n - 1, UnsameQ@## &, All] - 2; Array[f, 88] (* James C. McMahon, Mar 01 2025 *)

Crossrefs

Cf. A003261, A031286, A131838.

Sequence in context: A256707 A151963 A191291 * A309432 A230261 A242306

Adjacent sequences: A131838 A131839 A131840 * A131842 A131843 A131844

Keyword

easy,nonn,base

Author

Paolo P. Lava and Giorgio Balzarotti, Jul 20 2007

Extensions

Corrected entries and Maple code by Paolo P. Lava, Dec 19 2017

Status

approved