A073330 Let c(1)=n and c(k+1)=floor(c(k)/Pi) if c(k) is even, or c(k+1)=floor(Pi*c(k)) otherwise; sequence gives the smallest value a(n) such that c(a(n))=0.

7, 2, 6, 8, 18, 8, 14, 3, 5, 7, 9, 7, 9, 9, 17, 19, 23, 19, 31, 9, 13, 15, 17, 15, 17, 4, 6, 4, 22, 6, 10, 8, 14, 8, 12, 10, 12, 8, 10, 8, 10, 10, 14, 10, 14, 10, 16, 18, 22, 18, 20, 20, 22, 24, 26, 24, 28, 20, 30, 32, 36, 32, 36, 10, 12, 14, 16, 14, 16, 16, 20, 16, 22, 18, 22, 16

Offset

1,1

Links

Sean A. Irvine, Table of n, a(n) for n = 1..10000

Formula

Conjecture: sequence always exists (a(123456789)=61, a(2^30)=70) and there is a constant C=2.8... such that sum(k=1, n, a(k)) is asymptotic to C*n*Log(n)

Example

c(1)=1 => 3 => 9 => 28 => 8 => 2 => 0 => 0 => 0 ... hence a(1)=7.

Prog

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

Crossrefs

Sequence in context: A011361 A199433 A095398 * A208852 A248284 A350620

Adjacent sequences: A073327 A073328 A073329 * A073331 A073332 A073333

Keyword

easy,nonn

Author

Benoit Cloitre, Aug 22 2002

Status

approved