A155820 Primes of the form prime(k)^2 + 2*prime(k-1) where prime(k) is the k-th prime number.

13, 31, 59, 191, 887, 1019, 1931, 2903, 5471, 8087, 9587, 19031, 23099, 33119, 57587, 80651, 129587, 168083, 188351, 327179, 359987, 414731, 678971, 846383, 898691, 910103, 984047, 1040387, 1044479, 1132091, 1331711, 1411331, 1444787, 1517819, 1669259, 1909907

Offset

1,1

Links

Robert Israel, Table of n, a(n) for n = 1..10000

Example

prime(4)=7, prime(3)=5; 7^2+2*5=59, a prime. Hence 59 is a term.

Maple

count:= 0: q:= 2: R:= NULL:
while count < 100 do
  p:= q; q:= nextprime(q);
  v:= q^2 + 2*p;
  if isprime(v) then count:= count+1; R:= R, v; fi;
od:
R; # Robert Israel, Aug 22 2023

Mathematica

list = {}; Do[m = Prime[k]^2 + 2*Prime[k - 1]; If[PrimeQ[m], AppendTo[list, m]], {k, 2, 300}]; list (* Vaclav Kotesovec, Feb 14 2019 *)

Crossrefs

Cf. A000040.

Sequence in context: A301622 A166143 A065768 * A242231 A330855 A268927

Adjacent sequences: A155817 A155818 A155819 * A155821 A155822 A155823

Keyword

nonn

Author

Avik Roy (avik_3.1416(AT)yahoo.co.in), Jan 28 2009

Extensions

More terms from Vaclav Kotesovec, Feb 14 2019

Changed offset to 1 by Vaclav Kotesovec, Feb 14 2019

Status

approved