A124165 Primes p such that (2^p + 2^((p+1)/2) + 1)/5 is prime.

7, 17, 89, 1223, 5479, 11257, 11519, 12583, 23081, 36479, 52567, 52919, 125929, 365689, 1127239, 1148729, 4533073

Offset

1,1

Comments

PrimePi[ a(n) ] = {4, 7, 24, 200, 724, 1361, 1389, 1503, 2578, 3868, 5368, 5400, 11814, 31200, ...}.

3 terms found by David Broadhurst in Nov 2006: {36479, 52567, 52919}.

Only 2 terms found by Jean Penne in Nov 2006 belong to a(n): {125929, 365689}.

5 other numbers found by Jean Penne in Nov 2006 belong to related sequence of primes p such that (2^p - 2^((p+1)/2) + 1)/5 is prime: {221891, 235099, 305867, 311027, 333227}.

All terms belong to A124112 = {5, 7, 9, 11, 13, 17, 29, 43, 53, 89, 283, 557, 563, 613, 691, 1223, 2731, ...} (numbers k such that ((1+i)^k+1)/(2+i) is a Gaussian prime).

The terms 1127239 and 1148729 were found by Borys Jaworski in 2006-2007. - Alexander Adamchuk, Jun 20 2007

Links

Table of n, a(n) for n=1..17.

Henri Lifchitz and Renaud Lifchitz: PRP Records. Probable Primes Top 10000.

Mathematica

Do[p=Prime[n]; f=(2^p+2^((p+1)/2)+1)/5; If[PrimeQ[f], Print[{n, p}]], {n, 1, 200}]

Crossrefs

Cf. A124112 (numbers k such that ((1+i)^k+1)/(2+i) is a Gaussian prime.

Sequence in context: A035078 A359015 A177123 * A239150 A092057 A082738

Adjacent sequences: A124162 A124163 A124164 * A124166 A124167 A124168

Keyword

hard,more,nonn

Author

Alexander Adamchuk, Dec 02 2006, Dec 04 2006

Extensions

a(17) from Serge Batalov, Mar 31 2014

Status

approved