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
Keywords
Examples
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.
Links
- K. D. Bajpai, Table of n, a(n) for n = 1..10000
Programs
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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);
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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 *) -
PARI
for(n=1,10^3,if(ispseudoprime(k=prime(n+1)^2-prime(n)^2+1),print1(k", ")))