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A147545
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Primes of the form p*2^k+1 with k>0 and p=1 or p in this sequence.
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6
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3, 5, 7, 11, 13, 17, 23, 29, 41, 47, 53, 59, 83, 89, 97, 107, 113, 137, 167, 179, 193, 227, 233, 257, 353, 359, 389, 449, 467, 641, 719, 769, 773, 857, 929, 1097, 1283, 1409, 1433, 1439, 1553, 1697, 1889, 2657, 2819, 2879, 3089, 3329, 3593, 3617, 3779, 5639
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OFFSET
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1,1
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COMMENTS
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This sequence starts like A074781 but grows much faster. Observe that there can be large differences between consecutive terms. Can it be shown that there is always such a prime between consecutive powers of 2? Or that this sequence is infinite? By theorem 1 of the Noe paper, this sequence is a subsequence of A135832, primes in Section I of the phi iteration.
Sequence can be considered as a generalization of Fermat primes, A019434, which is a subsequence of this sequence.
All terms with binary weight k (A000120, at least 2 for these terms) can be found as a subset of primes found on the row k-1 of array A334100. E.g. primes with weight 2 are Fermat primes (A019434), those with weight 3 are A334092 (which doesn't contain any other primes), those with weight 4 are in A334093 (among also other kind of primes), those with weights 5, 6, 7 are included as (proper) subsets in A334094, A334095 and A334096 respectively. (End)
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LINKS
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FORMULA
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MATHEMATICA
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nn=2^13; t={1}; i=1; While[q=t[[i]]; k=1; While[p=1+q*2^k; p<nn, If[PrimeQ[p], AppendTo[t, p]]; k++ ]; i<Length[t], i++ ]; t=Rest[Sort[t]]
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PROG
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(PARI)
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CROSSREFS
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KEYWORD
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nonn
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AUTHOR
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STATUS
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approved
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