A090612 Numbers k such that the k-th prime is of the form 2*j^2 + 1.

2, 8, 21, 38, 153, 191, 232, 279, 327, 378, 493, 559, 1086, 1272, 1360, 1769, 1989, 2111, 2224, 2344, 2471, 3272, 3721, 3863, 4838, 5006, 5359, 6291, 6871, 7077, 7909, 8127, 9245, 9928, 10654, 10889, 12164, 12957, 13764, 14881, 16034, 16343, 16944

Offset: 1

Author

Ray Chandler, Dec 21 2003

Keywords

• nonn

Comments

A090698 indexed by A000040.

Examples

			From _Jon E. Schoenfield_, Jan 24 2018: (Start)
prime(8) = 19 = 2*3^2 + 1, so 8 is in the sequence.
prime(21) = 73 = 2*6^2 + 1, so 21 is in the sequence.
prime(33) = 137 = 2*68 + 1, and 68 is not a square, so 33 is not in the sequence. (End)
		

Links

• Robert Israel, Table of n, a(n) for n = 1..1525

Crossrefs

Cf. A089001, A089008, A090698.

Programs

Maple

N:= 1000; # to get all entries corresponding to primes <= 2*N^2+1.
R:= select(isprime,[seq(2*k^2+1,k=1..N)]):
A090612:= map(numtheory[pi],R); # Robert Israel, May 09 2014

Mathematica

Select[Range[18000],IntegerQ[Sqrt[(Prime[#]-1)/2]]&] (* Harvey P. Dale, Apr 25 2016 *)

Formula

a(n)=k such that A000040(k) = A090698(n) = 2*A089001(n)^2 + 1.