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Search: id:A163427
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| A163427 |
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Primes p such that (p+1)^3/8+(p-1)/2 are also prime numbers. |
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5
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| 5, 7, 13, 19, 29, 31, 41, 53, 71, 101, 103, 109, 173, 191, 199, 223, 229, 233, 239, 257, 269, 277, 331, 383, 397, 431, 491, 569, 571, 599, 619, 631, 719, 733, 751, 757, 761, 823, 857, 859, 863, 887, 907, 937, 967, 971, 977, 1009, 1019, 1063, 1069, 1123, 1163
(list; graph; listen)
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OFFSET
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1,1
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COMMENT
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Primes A000040(k) such that (A006254(k-1))^3+ A005097(k-1) are also prime numbers.
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FORMULA
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(a(n)+1)^3/8+(a(n)-1)/2 = A163426(n).
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EXAMPLE
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For p=5, (5+1)^3/8+(5-1)/2=27+2=29, prime, which adds p=5 to the sequence.
For p=7, (7+1)^3/8+(7-1)/2=67, prime, which adds p=7 to the sequence.
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MATHEMATICA
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f[n_]:=((p+1)/2)^3+((p-1)/2); lst={}; Do[p=Prime[n]; If[PrimeQ[f[p]], AppendTo[lst, p]], {n, 6!}]; lst
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CROSSREFS
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Cf. A162652, A163418, A163419, A163420, A163421, A163422, A163424, A163425, A163426
Sequence in context: A124661 A084932 A038908 this_sequence A164567 A045443 A153116
Adjacent sequences: A163424 A163425 A163426 this_sequence A163428 A163429 A163430
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KEYWORD
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nonn
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AUTHOR
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Vladimir Orlovsky (4vladimir(AT)gmail.com), Jul 27 2009
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EXTENSIONS
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Edited by R. J. Mathar (mathar(AT)strw.leidenuniv.nl), Aug 24 2009
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