A131840 Additive persistence of Cullen numbers.

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

Offset

1,4

Links

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

Formula

a(n) = A031286(A002064(n)). - James C. McMahon, Mar 01 2025

Example

Cullen number 385 --> 3+8+5=16 -->1+6=7 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. A002064, A031286, A131837.

Sequence in context: A073610 A285797 A362746 * A179752 A085693 A067995

Adjacent sequences: A131837 A131838 A131839 * A131841 A131842 A131843

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