A305412 -id:A305412 - cp's OEIS frontend

A094810 Primes of the form F(n)*F(n+1)+F(n+2).

3, 5, 11, 23, 53, 307, 769, 5039, 13049, 603667, 1578823, 10810469, 427860443429, 16944504081930151, 31525215457325198354227

Offset: 1

Giovanni Teofilatto, Jun 11 2004

nonn

Excluding the term a(4)=23, primes p such that p(n) is not a sum of two squares but p(n+1) is a sum of two squares.

lista(nn) = {for (n=1, nn, if (isprime(p=fibonacci(n)*fibonacci(n+1) +fibonacci(n+2)), print1(p, ", ")););} \\ Michel Marcus, Jun 03 2013

is in the sequence because F(2)*F(3)+F(4) = 1*2+3=5.
is in because F(3)*F(4)+F(5) = 2*3+5 = 11
is in because F(4)*F(5)+F(6) = 3*5+8 = 23
A000040 INTERSECT A305412. - R. J. Mathar, Nov 14 2019

More terms from Michel Marcus, Jun 03 2013

A305414 Numbers k such that F(k)*F(k+1) + F(k+2) is a prime, where F = A000045 (Fibonacci numbers).

Original entry on oeis.org

1, 2, 3, 4, 5, 7, 8, 10, 11, 15, 16, 18, 29, 40, 55, 134, 159, 261, 276, 519, 1792, 2045, 2111, 2830, 2878, 3575, 6301, 7394, 9432, 13558, 19714, 21396, 25731, 26790, 28792, 32070, 33951, 46997, 63134, 66272, 67619, 70448, 75525, 77994, 90437

Offset: 1

Vincenzo Librandi, Jun 09 2018

nonn

Primes in A305412.

a(46) > 10^5. - Robert Price, Jun 18 2018

Cf. A000045, A305412.

[n: n in [1..1500] | IsPrime(Fibonacci(n) * Fibonacci(n+1) + Fibonacci(n+2))];

Select[Range[1000], PrimeQ[(Fibonacci[#] Fibonacci[# + 1] + Fibonacci[# + 2])]&]

More terms from Vaclav Kotesovec, Jun 11 2018
a(39) from Giovanni Resta, Jun 11 2018
a(40)-a(45) from Robert Price, Jun 18 2018

cp's OEIS Frontend

A094810 Primes of the form F(n)*F(n+1)+F(n+2).

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