A090612 - OEIS

%I #13 Jan 26 2018 03:58:50

%S 2,8,21,38,153,191,232,279,327,378,493,559,1086,1272,1360,1769,1989,

%T 2111,2224,2344,2471,3272,3721,3863,4838,5006,5359,6291,6871,7077,

%U 7909,8127,9245,9928,10654,10889,12164,12957,13764,14881,16034,16343,16944

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

%C A090698 indexed by A000040.

%H Robert Israel, <a href="/A090612/b090612.txt">Table of n, a(n) for n = 1..1525</a>

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

%e From _Jon E. Schoenfield_, Jan 24 2018: (Start)

%e prime(8) = 19 = 2*3^2 + 1, so 8 is in the sequence.

%e prime(21) = 73 = 2*6^2 + 1, so 21 is in the sequence.

%e prime(33) = 137 = 2*68 + 1, and 68 is not a square, so 33 is not in the sequence. (End)

%p N:= 1000; # to get all entries corresponding to primes <= 2*N^2+1.

%p R:= select(isprime,[seq(2*k^2+1,k=1..N)]):

%p A090612:= map(numtheory[pi],R); # _Robert Israel_, May 09 2014

%t Select[Range[18000],IntegerQ[Sqrt[(Prime[#]-1)/2]]&] (* _Harvey P. Dale_, Apr 25 2016 *)

%Y Cf. A089001, A089008, A090698.

%K nonn

%O 1,1

%A _Ray Chandler_, Dec 21 2003