A111497 Difference between successive terms of floor(10^n/Li(10^n) - 1).

2, 3, 2, 2, 2, 2, 3, 2, 2, 3, 2, 3, 2, 2, 3, 2, 3, 2, 2, 3, 2, 2, 2, 2, 3, 2, 2, 2, 2, 3, 2, 2, 2, 2, 3, 2, 2, 2, 2, 3, 2, 2, 3, 2, 3, 2, 2, 3, 2, 3, 2, 2, 3, 2, 3, 2, 2, 3, 2, 2, 2, 2, 3, 2, 2, 2, 2, 3, 2, 2, 2, 2, 3, 2, 2, 2, 2, 3, 2, 2, 3, 2, 3, 2, 2, 3, 2, 3, 2, 2, 3, 2, 3, 2, 2, 3, 2, 2, 2, 2

Offset

1,1

Comments

10^n/Li(10^n) - 1) is the ratio of estimated composite numbers less than 10^n to the estimated prime numbers less than 10^n. Conjecture: 2 and 3 are the only numbers in this sequence.

Links

Table of n, a(n) for n=1..100.

Formula

Li(n) is the logarithmic integral which approximates the number of primes less than n. n Li(n) = Int dt/log(t) 2

Prog

(PARI) LiRatioDiff(m, n) = { local(x, p1, p2, a, b); forstep(x=m, n, 2, p1=10.^x; p2=10^(x+1); a=floor(p1/Li(p1)-1); b=floor(p2/Li(p2)-1); print1(b-a, ", ") ) } Li(x) = \ Logarithmic integral { -eint1(log(1/x)) }

Crossrefs

Sequence in context: A368859 A338238 A355077 * A220554 A208243 A209320

Adjacent sequences: A111494 A111495 A111496 * A111498 A111499 A111500

Keyword

easy,nonn

Author

Cino Hilliard, Nov 16 2005

Status

approved