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

1,1

Links

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

Example

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

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 *)

Prog

(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

Crossrefs

Cf. A072669.

Sequence in context: A299103 A201961 A142145 * A043427 A038485 A077722

Adjacent sequences: A227337 A227338 A227339 * A227341 A227342 A227343

Keyword

nonn

Author

K. D. Bajpai, Jul 07 2013

Status

approved