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A163424 Primes of the form (p-1)^3/8 + (p+1)^2/4 where p is prime. 8
5, 17, 43, 593, 829, 2969, 3631, 12743, 27961, 44171, 60919, 127601, 278981, 578843, 737281, 950993, 980299, 1455893, 1969001, 2424329, 2763881, 3605293, 5767739, 7801993, 9305521, 11290049, 12220361, 12704093, 16452089, 22987529, 35720189 (list; graph; refs; listen; history; text; internal format)
OFFSET
1,1
LINKS
EXAMPLE
(3-1)^3/8 + (3+1)^2/4 = 1 + 4 = 5;
(5-1)^3/8 + (5+1)^2/4 = 8 + 9 = 17;
(7-1)^3/8 + (7+1)^2/4 = 27 + 16 = 43.
MATHEMATICA
f[n_]:=((p-1)/2)^3+((p+1)/2)^2; lst={}; Do[p=Prime[n]; If[PrimeQ[f[p]], AppendTo[lst, f[p]]], {n, 7!}]; lst
Select[(#-1)^3/8+(#+1)^2/4&/@Prime[Range[150]], PrimeQ] (* Harvey P. Dale, Oct 05 2018 *)
PROG
(PARI) list(lim)=my(v=List(), t); forprime(p=3, , t=((p-1)/2)^3 + ((p+1)/2)^2; if(t>lim, break); if(isprime(t), listput(v, t))); Vec(v) \\ Charles R Greathouse IV, Dec 23 2016
CROSSREFS
Subsequence of A100662.
For the corresponding primes p, see A163425.
Sequence in context: A146778 A146858 A146183 * A294102 A190969 A099451
KEYWORD
nonn,easy
AUTHOR
STATUS
approved

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Last modified February 29 17:04 EST 2024. Contains 370427 sequences. (Running on oeis4.)