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A139474
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a(n)=((2*Sqrt[2] + 3)^(2^(Prime[n] - 1) - 1) - (3 - 2*Sqrt[2])^(2^(Prime[n] - 1) - 1))/(4*Sqrt[2]).
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5
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OFFSET
| 1,2
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COMMENTS
| Next term a(5) has 783 decimal digits
Conjecture of Kenneth J. Ramsey (RamseyKK2(AT)aol.com) from May 16 2006 (see A001109): a(n) is divisible by 2^Prime[n]-1 if and only 2^Prime[n]-1 is Mersenne prime
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MATHEMATICA
| Table[Expand[((2*Sqrt[2] + 3)^(2^(Prime[n] - 1) - 1) - (3 - 2*Sqrt[2])^(2^(Prime[n] - 1) - 1))/(4*Sqrt[2])], {n, 1, 10}] (*Artur Jasinski*)
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CROSSREFS
| Cf. A001109, A139474, A139475, A139476.
Sequence in context: A110596 A126029 A107736 * A023929 A010113 A167264
Adjacent sequences: A139471 A139472 A139473 * A139475 A139476 A139477
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KEYWORD
| nonn
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AUTHOR
| Artur Jasinski (grafix(AT)csl.pl), Apr 22 2008
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