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A163428 Primes of the form ((p+1)/2)^3 + ((p-1)/2)^2 where p is prime. 4
31, 73, 241, 379, 3571, 9661, 20359, 47881, 51949, 65521, 119953, 135151, 291721, 427351, 736921, 761671, 921889, 1202041, 1494313, 1533871, 1742161, 1785961, 2478331, 2533681, 3197839, 3820441, 3894229, 4044643, 4855033, 6573799 (list; graph; refs; listen; history; text; internal format)
OFFSET
1,1
COMMENTS
Primes of the form k^3 + k^2 - 2k + 1 where 2k-1 is prime.
LINKS
EXAMPLE
((5+1)/2)^3 + ((5-1)/2)^2 = 27 + 4 = 31, ((7+1)/2)^3 + ((7-1)/2)^2 = 64 + 9 = 73
MAPLE
res:= NULL:
count:= 0:
p:= 2
while count < 100 do
p:= nextprime(p);
r:= ((p+1)/2)^3 + ((p-1)/2)^2;
if isprime(r) then
res:= res, r;
count:= count+1;
fi
od:
res; # Robert Israel, Oct 10 2016
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, 6!}]; lst
PROG
(PARI) lista(nn) = forprime(p=3, nn, if (isprime(q=((p+1)/2)^3 + ((p-1)/2)^2), print1(q, ", "))); \\ Michel Marcus, Oct 11 2016
CROSSREFS
Sequence in context: A141892 A298613 A155933 * A130468 A068917 A317053
KEYWORD
nonn,easy
AUTHOR
EXTENSIONS
Description and edits by Charles R Greathouse IV, Oct 05 2009
STATUS
approved

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Last modified February 26 05:55 EST 2024. Contains 370335 sequences. (Running on oeis4.)