A122487 2 together with odd primes p that divide Fibonacci[(p+1)/2].

2, 13, 17, 37, 53, 73, 97, 113, 137, 157, 173, 193, 197, 233, 257, 277, 293, 313, 317, 337, 353, 373, 397, 433, 457, 557, 577, 593, 613, 617, 653, 673, 677, 733, 757, 773, 797, 853, 857, 877, 937, 953, 977, 997, 1013, 1033, 1093, 1097, 1117, 1153, 1193, 1213

Offset: 1

Author

Alexander Adamchuk, Sep 16 2006

Keywords

• nonn
• easy

Comments

Primes of the form 2x^2+2xy+13y^2. Discriminant = -100. - T. D. Noe, May 02 2008

Primes of the form a^2 + b^2 such that a^2 == b^2 (mod 5). - Thomas Ordowski, May 18 2015

Links

• Giovanni Resta, Table of n, a(n) for n = 1..1000

Crossrefs

Cf. A000045, A033205, A045468, A003631, A053028, A139827.

Programs

Mathematica

Select[Prime[Range[1000]],IntegerQ[Fibonacci[(#1+1)/2]/#1]&]

PARI

is(n)=my(k=n%20); (k==13||k==17||k==2) && isprime(n) \\ Charles R Greathouse IV, May 18 2015

Formula

Except for 2, the primes are congruent to {13, 17} (mod 20). - T. D. Noe, May 02 2008

2 together with all primes p == {13, 17} (mod 20). - Thomas Ordowski, May 18 2015

Extensions

Definition changed by T. D. Noe, May 02 2008