proposed

approved

editing

proposed

0, 0, 1, 2, 1, 2, 2, 2, 3, 1, 2, 2, 3, 2, 2, 2, 2, 3, 2, 3, 3, 2, 2, 3, 2, 2, 2, 2, 3, 2, 3, 2, 3, 2, 3, 3, 2, 2, 3, 3, 3, 2, 3, 2, 3, 3, 3, 3, 2, 3, 3, 3, 3, 3, 3, 3, 3, 3, 2, 3, 3, 2, 3, 4, 3, 3, 3, 3, 2, 3, 2, 3, 3, 2, 3, 3, 3, 3, 3, 2, 3, 2, 2, 2, 2, 3, 2, 2, 3, 3, 3, 3, 2, 2, 2, 2, 3, 2, 3, 2, 2, 2, 2, 3, 2, 3, 3, 2, 3, 2, 3, 3, 2

P:=proc(n) local i, k, w, ok, cont; for i from 1 by 1 to n do w:=0; k:=i*2^i+1; ok:=1; if k<10 then print(0); else cont:=1; while ok=1 do while k>0 do w:=w+(k-(trunc(k/10)*10)); k:=trunc(k/10); od; if w<10 then ok:=0; print(cont); else cont:=cont+1; k:=w; w:=1; fi; od; fi; od; end: P(120);

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);

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

approved

editing

_Paolo P. Lava & _ and _Giorgio Balzarotti (paoloplava(AT)gmail.com), _, Jul 20 2007

Paolo P. Lava & Giorgio Balzarotti (pplpaoloplava(AT)splgmail.atcom), Jul 20 2007

Additive persistence of Cullen numbers.

0, 0, 1, 2, 1, 2, 2, 2, 3, 1, 2, 2, 3, 2, 2, 2, 2, 3, 3, 3, 2, 3, 2, 2, 2, 2, 3, 2, 3, 2, 3, 3, 3, 2, 2, 3, 3, 3, 2, 3, 2, 3, 3, 3, 3, 2, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 4, 3, 3, 3, 3, 2, 3, 2, 3, 3, 2, 3, 3, 3, 3, 3, 2, 3, 2, 2, 2, 2, 3, 2, 2, 3, 3, 3, 3, 2, 2, 2, 2, 3, 2, 3, 2, 2, 2, 2, 3, 2, 3, 3, 3, 3, 3

1,4

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

P:=proc(n) local i, k, w, ok, cont; for i from 1 by 1 to n do w:=0; k:=i*2^i+1; ok:=1; if k<10 then print(0); else cont:=1; while ok=1 do while k>0 do w:=w+(k-(trunc(k/10)*10)); k:=trunc(k/10); od; if w<10 then ok:=0; print(cont); else cont:=cont+1; k:=w; w:=1; fi; od; fi; od; end: P(120);

Cf. A002064, A131837.

easy,nonn,base

Paolo P. Lava & Giorgio Balzarotti (ppl(AT)spl.at), Jul 20 2007

approved