A229496 Primes p of the form prime(n+1)^2-prime(n)^2+1.

17, 73, 73, 313, 409, 313, 601, 673, 241, 769, 1033, 1489, 409, 433, 3361, 1033, 1609, 601, 1321, 2113, 769, 5209, 1801, 2833, 3049, 3121, 1129, 2473, 1249, 2521, 6841, 4273, 4441, 4513, 3049, 6481, 8521, 5233, 3529, 3673, 11353, 6073, 2089, 6529, 6793, 2281, 7321

Offset

1,1

Links

K. D. Bajpai, Table of n, a(n) for n = 1..10000

Example

a(1)=17:  prime(2+1)^2-prime(2)^2+1= 17,  which is prime.
a(6)=313:  prime(12+1)^2-prime(12)^2+1= 313,  which is prime.

Maple

KD:= proc() local a, b, c, d; a:=ithprime(n+1)^2-ithprime(n)^2+1; if isprime(a) then RETURN(a): fi; end:seq(KD(), n=1..500);

Mathematica

Select[Table[Prime[n + 1]^2 - Prime[n]^2 + 1, {n, 10^3}], PrimeQ[#] &]
Select[#[[2]]-#[[1]]+1&/@Partition[Prime[Range[200]]^2, 2, 1], PrimeQ] (* Harvey P. Dale, May 21 2021 *)

Prog

(PARI) for(n=1, 10^3, if(ispseudoprime(k=prime(n+1)^2-prime(n)^2+1), print1(k", ")))

Crossrefs

Cf. A176136, A069482.

Sequence in context: A130748 A131692 A157864 * A268544 A059704 A269727

Adjacent sequences: A229493 A229494 A229495 * A229497 A229498 A229499

Keyword

nonn

Author

K. D. Bajpai, Sep 25 2013

Status

approved