A206328 Primes of the form n^2+1 such that (n+2)^2+1 is also prime.

5, 17, 197, 577, 2917, 15377, 41617, 147457, 215297, 401957, 414737, 509797, 1196837, 1308737, 1378277, 1547537, 1623077, 1726597, 1887877, 2446097, 2604997, 2802277, 2835857, 3857297, 4218917, 4343057, 4384837, 5779217, 6022117, 6421157, 7096897, 8031557

Offset: 1

Author

Michel Lagneau, Feb 06 2012

Keywords

• nonn
• easy

Comments

Primes corresponding to A096012 and subset of A002496.

For n > 1, a(n) ==7 (mod 10) because n ==4 (mod 10).

Conjecture: this sequence is infinite.

Examples

			For n = 4, n^2 + 1 = 17 is prime and  (n+2)^2 + 1 = 37 is also prime => 17 is in the sequence.
		

Links

• Harvey P. Dale, Table of n, a(n) for n = 1..1000

Crossrefs

Cf. A096012, A002496.

Programs

Maple

for n from 1 to 4000 do: x:=n^2+1:y:=(n+2)^2+1:if type(x,prime)=true and type(y,prime)=true then printf(`%d, `,x): else fi:od:

Mathematica

Select[Partition[Range[3000]^2+1,3,1],AllTrue[{#[[1]],#[[3]]},PrimeQ]&][[All,1]] (* Harvey P. Dale, Jan 16 2023 *)