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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)).
5
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.
CROSSREFS
KEYWORD
nonn
AUTHOR
Gary W. Adamson, Apr 04 2004
EXTENSIONS
Edited by Don Reble, Nov 14 2005
STATUS
approved