A093608 Let b(0)=1; b(1)=1; b(n+2)=(e^g+1/e^g)*b(n+1)-b(n). a(n)=floor(b(n)).

1, 1, 2, 3, 6, 11, 20, 36, 64, 115, 205, 366, 652, 1162, 2070, 3687, 6567, 11696, 20832, 37103, 66084, 117701, 209635, 373375, 665008, 1184428, 2109552, 3757265, 6691962, 11918868, 21228368, 37809262, 67341034, 119939258, 213620504

Offset

0,3

Comments

g is Euler's gamma, 0.5772156649...

a(n+1)/a(n) converges to e^g.

Young states, "It has been argued on probabilistic grounds that the expected number of primes p in the octave interval (x,2x) for which 2^p-1 is a prime is e^G where G is Euler's constant. Equivalently: If M(n) is the n-th Mersenne prime, then (log to base 2): log log M(n)/n ==> e^(-G)."

References

Robert M. Young, "Excursions in Calculus, An Interplay of the Continuous and the Discrete", MAA, 1992, p. 245.

Links

Table of n, a(n) for n=0..34.

Crossrefs

Cf. A090039, A090426, A090427, A093607.

Sequence in context: A352500 A002985 A239342 * A320328 A079976 A017992

Adjacent sequences: A093605 A093606 A093607 * A093609 A093610 A093611

Keyword

nonn

Author

Gary W. Adamson, Apr 04 2004

Extensions

Edited by Don Reble, Nov 14 2005

Status

approved