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

Author

Paolo P. Lava and Giorgio Balzarotti, Jul 20 2007

Keywords

• easy
• nonn
• base

Examples

			Cullen number 385 --> 3+8+5=16 -->1+6=7 thus persistence is 2
		

Crossrefs

Cf. A002064, A031286, A131837.

Programs

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 *)

Formula

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

Extensions

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