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A178490
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Primes of the form 2*p^k-1, where p is prime and k >= 1.
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4
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3, 5, 7, 13, 17, 31, 37, 53, 61, 73, 97, 127, 157, 193, 241, 277, 313, 337, 397, 421, 457, 541, 577, 613, 661, 673, 733, 757, 877, 997, 1093, 1153, 1201, 1213, 1237, 1249, 1321, 1381, 1453, 1621, 1657, 1753, 1873, 1933, 1993, 2017, 2137, 2341, 2473, 2557, 2593
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OFFSET
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1,1
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COMMENTS
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Includes the Mersenne primes > 3 (A000668) and primes of the form 2p^2-1 (A092057) and 2p-1 (A005383) as subsequences; excluding the latter yields A178491.
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LINKS
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EXAMPLE
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a(1) = 7 = 2*2^2-1 and a(2) = 17 = 2*3^2-1 are also in A092057, and a(3) = 31 = 2*2^4-1 = A000668(3), but a(4) = 53 = 2*3^3-1 is in neither of these subsequences.
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MAPLE
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filter:= n -> isprime(n) and nops(numtheory:-factorset((n+1)/2))=1:
select(filter, [seq(i, i=3..10000, 2)]); # Robert Israel, Feb 20 2024
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MATHEMATICA
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Select[Prime[Range[20000]], Length[FactorInteger[(#+1)/2]]==1&]
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PROG
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(PARI) is_A178490(n) = isprime(n) & omega((n+1)\2)==1
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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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