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A203074
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a(0)=1; for n>0, a(n) = next prime after 2^(n-1).
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4
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1, 2, 3, 5, 11, 17, 37, 67, 131, 257, 521, 1031, 2053, 4099, 8209, 16411, 32771, 65537, 131101, 262147, 524309, 1048583, 2097169, 4194319, 8388617, 16777259, 33554467, 67108879, 134217757, 268435459, 536870923, 1073741827, 2147483659
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OFFSET
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0,2
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COMMENTS
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Equals {1} union A014210. Unlike A014210, every positive integer can be written in one or more ways as a sum of terms of this sequence. See A203075, A203076.
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LINKS
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M. F. Hasler, Table of n, a(n) for n = 0..1300
Wikipedia, Complete sequence.
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FORMULA
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A203074(n) = 2^(n-1)+A013597(n-1), for n>0. - M. F. Hasler, Mar 15 2012
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EXAMPLE
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a(5) = 17, since this is the next prime after 2^(5-1) = 2^4 = 16.
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MATHEMATICA
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nextprime[n_Integer] := (k=n+1; While[!PrimeQ[k], k++]; k); aprime[m_Integer] := (If[m==0, 1, nextprime[2^(m-1)]]); Table[aprime[l], {l, 0, 100}]
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PROG
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(PARI) a(n)=if(n, nextprime(2^n/2+1), 1) \\ Charles R Greathouse IV
(PARI) A203074(n)=nextprime(2^(n-1)+1)-!n \\ - M. F. Hasler, Mar 15 2012
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CROSSREFS
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Cf. A013632, A013597, A014210, A203075, A203076.
Sequence in context: A175247 A079370 A014210 * A014556 A062737 A085613
Adjacent sequences: A203071 A203072 A203073 * A203075 A203076 A203077
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KEYWORD
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nonn
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AUTHOR
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Frank M. Jackson and N. J. A. Sloane, Dec 28 2011.
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STATUS
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approved
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