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A156589
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a(n) = 4^n - 2^n - 1.
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2
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-1, 1, 11, 55, 239, 991, 4031, 16255, 65279, 261631, 1047551, 4192255, 16773119, 67100671, 268419071, 1073709055, 4294901759, 17179738111, 68719214591, 274877382655, 1099510579199, 4398044413951, 17592181850111, 70368735789055
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OFFSET
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0,3
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COMMENTS
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Sequence A098845 lists indices of primes, i.e., a(n) prime <=> n=A098845(k) for some k.
Starting with n=2, binary numbers of the form (n-1)0(n) where n is the index and the number of 1's. It can also be formed by appending a 1 to the right of each term of A129868.
1/a(n) = Sum_{m>0} A000045(m)*2^(-n(m+1)) for n > 0. E.g., 1/a(4) = 0.0000 0001 0001 0010 0011 0101 1000 ... in binary. - Lee A. Newberg, Apr 12 2018
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LINKS
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FORMULA
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G.f.: ( 1-8*x+10*x^2 ) / ( (-1+x)*(2*x-1)*(4*x-1) ). - R. J. Mathar, Oct 21 2014
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MATHEMATICA
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PROG
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(PARI) vector(99, n, 4^n-2^n-1)
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CROSSREFS
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KEYWORD
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sign,easy
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AUTHOR
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STATUS
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approved
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