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A163427 Primes p such that (p+1)^3/8+(p-1)/2 is also prime. 4
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; refs; listen; history; text; internal format)
OFFSET

1,1

COMMENTS

Primes A000040(k) such that (A006254(k-1))^3+ A005097(k-1) is also prime.

LINKS

Vincenzo Librandi, Table of n, a(n) for n = 1..1000

FORMULA

(a(n)+1)^3/8+(a(n)-1)/2 = A163426(n).

EXAMPLE

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.

MATHEMATICA

f[n_]:=((p+1)/2)^3+((p-1)/2); lst={}; Do[p=Prime[n]; If[PrimeQ[f[p]], AppendTo[lst, p]], {n, 6!}]; lst

Select[Prime[Range[100]], PrimeQ[(# + 1)^3 / 8 + (# - 1) / 2]&] (* Vincenzo Librandi, Apr 09 2013 *)

PROG

(MAGMA) [p: p in PrimesInInterval(3, 1200) | IsPrime((p+1)^3 div 8+(p-1) div 2)]; // Vincenzo Librandi, Apr 09 2013

CROSSREFS

Cf. A162652, A163418, A163419, A163420, A163421, A163422, A163424, A163425, A163426.

Sequence in context: A314327 A215804 A274242 * A215805 A339692 A164567

Adjacent sequences:  A163424 A163425 A163426 * A163428 A163429 A163430

KEYWORD

nonn,easy

AUTHOR

Vladimir Joseph Stephan Orlovsky, Jul 27 2009

EXTENSIONS

Edited by R. J. Mathar, Aug 24 2009

STATUS

approved

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Last modified October 19 21:22 EDT 2021. Contains 348091 sequences. (Running on oeis4.)