A227340 Primes of the form p^2 + q^2 - 1 where p and q are consecutive primes.

73, 457, 1801, 3049, 3529, 4057, 8209, 10369, 19609, 20809, 33289, 41521, 51217, 84121, 103969, 111409, 115201, 121081, 129049, 141529, 150169, 155689, 180097, 223129, 282769, 308929, 342841, 397849, 426889, 432457, 627217, 649801, 658969, 710449, 729649

Offset: 1

Author

K. D. Bajpai, Jul 07 2013

Keywords

• nonn

Examples

			a(1) = 5^2 + 7^2 - 1 = 73, which is prime.
		

Links

• Charles R Greathouse IV, Table of n, a(n) for n = 1..10000

Crossrefs

Cf. A072669.

Programs

Maple

K := proc(x) local a; a:=ithprime(x)^2+ithprime(x+1)^2-1; if (isprime(a))then RETURN (a) fi: end: seq(K(x), x=1..500); # K. D. Bajpai, Jul 07 2013
K:=proc()local x,a,c; c:=1; for x from 1 to 5000 do; a:=ithprime(x)^2+ithprime(x+1)^2-1;if isprime(a) then lprint(c,a);c:=c+1;fi;od; end: K(); # K. D. Bajpai, Jul 07 2013

Mathematica

t = {}; Do[p = Prime[n]; q = Prime[n + 1]; p2 = p^2 + q^2 - 1; If[PrimeQ[p2], AppendTo[t, p2]], {n, 200}]; t (* T. D. Noe, Jul 09 2013 *)

PARI

is(n)=if(isprime(n), my(x=sqrtint((n+1)\2)); nextprime(x+1)^2 +precprime(x)^2==n+1 && n>3, 0) \\ Charles R Greathouse IV, Jul 08 2013

PARI

p=2;forprime(q=3,1e5,if(isprime(t=p^2+q^2-1),print1(t", "));p=q) \\ Charles R Greathouse IV, Jul 08 2013