A073369 Let c(1)=n, e=2.71... and c(k+1)=floor(c(k)/e) if c(k) is even, c(k+1)=floor(e*c(k)) otherwise; sequence gives the smallest value a(n) such that c(a(n))=0.

3, 2, 4, 4, 12, 3, 9, 3, 5, 5, 9, 5, 11, 13, 15, 13, 15, 4, 8, 10, 14, 4, 6, 4, 8, 6, 10, 6, 8, 10, 12, 10, 18, 6, 10, 12, 14, 12, 14, 14, 20, 16, 18, 14, 16, 14, 26, 16, 24, 5, 7, 9, 11, 9, 15, 11, 13, 15, 17, 5, 9, 5, 9, 7, 9, 5, 7, 9, 13, 9, 11, 7, 9, 11, 21, 11, 15, 7, 9, 9, 11, 11, 17

Offset

1,1

Links

Table of n, a(n) for n=1..83.

Formula

Conjecture: sequence always exists and there is a constant C=2.9... such that sum(k=1, n, a(k)) is asymptotic to C*n*Log(n). Is this constant the same as those for the sequence involving Pi instead of e?

Prog

(PARI) P=exp(1); a(n)=if(n<0, 0, s=n; t=2; while(floor(s/P^(-1)^s)>0, s=floor(s/P^(-1)^s); t++); t)

Crossrefs

Sequence in context: A365613 A338315 A240541 * A021759 A070221 A020814

Adjacent sequences: A073366 A073367 A073368 * A073370 A073371 A073372

Keyword

easy,nonn

Author

Benoit Cloitre, Aug 23 2002

Status

approved