A182434 Number of primes p < n such that 4*p+1 is also prime.

0, 0, 1, 1, 1, 1, 2, 2, 2, 2, 2, 2, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 4, 4, 4, 4, 4, 4, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 6, 6, 6, 6, 6, 6, 7, 7, 7, 7, 7, 7, 8, 8, 8, 8, 8, 8, 8, 8, 8

Offset: 1

Author

Enrique Pérez Herrero, Apr 28 2012

Keywords

• nonn

Links

• Enrique Pérez Herrero, Table of n, a(n) for n = 1..10000

Crossrefs

Cf. A023212, A182265.

Cf. A005384, A156660, A156874, A092816.

Programs

Mathematica

Accumulate[Table[Boole[PrimeQ[n]&&PrimeQ[4n+1]],{n,1,200}]]
Accumulate[If[AllTrue[{#,4#+1},PrimeQ],1,0]&/@Range[90]] (* The program uses the AllTrue function from Mathematica version 10 *) (* Harvey P. Dale, Feb 26 2015 *)

Formula

a(10^n) = A182265(n).

a(n) = sum(i=2..n, floor(phi(4*i^2+i)/(4*i^2-4*i))). - Enrique Pérez Herrero, May 02 2012.