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A124165 Primes p such that (2^p + 2^((p+1)/2) + 1)/5 is prime. 4
7, 17, 89, 1223, 5479, 11257, 11519, 12583, 23081, 36479, 52567, 52919, 125929, 365689, 1127239, 1148729, 4533073 (list; graph; refs; listen; history; text; internal format)
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 a(n) belong to A124112(n) = {5, 7, 9, 11, 13, 17, 29, 43, 53, 89, 283, 557, 563, 613, 691, 1223, 2731, ...} Numbers n such that ((1+I)^n+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 & 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 n such that ((1+I)^n+1)/(2+I) is a Gaussian prime.

Sequence in context: A123206 A035078 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

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Last modified November 19 03:40 EST 2019. Contains 329310 sequences. (Running on oeis4.)