A229075 Primes of the form p^2 + q^2 + 21, where p and q are consecutive primes.

191, 311, 479, 911, 1823, 2351, 4079, 5039, 6311, 8231, 9551, 10391, 13151, 14831, 17351, 22079, 24671, 33311, 35951, 41543, 51239, 57839, 61991, 69263, 73751, 76079, 84143, 101279, 103991, 106751, 111431, 115223, 141551, 145823, 198479, 210071, 223151, 263591

Offset: 1

Author

K. D. Bajpai, Sep 12 2013

Keywords

• nonn

Comments

Conjecture: the expression p^2+q^2+c with p and q consecutive primes and c=21 generates more primes than any other value of c in the range 1..150. Hence, c=21 is considered for this sequence.

Examples

			a(1) = 191: prime(4)^2 + prime(4+1)^2 + 21 = 191, which is prime.
		

Links

• K. D. Bajpai, Table of n, a(n) for n = 1..5000

Crossrefs

Cf. A072669, A227340.

Programs

Maple

KD:= proc() local a; a:= ithprime(n)^2+ithprime(n+1)^2+21;  if isprime(a) then RETURN(a):  fi;  end: seq(KD(),n=1..300);

Mathematica

Select[Table[Prime[n]^2 + Prime[n + 1]^2 + 21, {n, 100}], PrimeQ] (* T. D. Noe, Sep 12 2013 *)