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

1,1

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.

Links

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

Example

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

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 *)

Crossrefs

Cf. A096012, A002496.

Sequence in context: A164740 A053678 A090645 * A096407 A216428 A062230

Adjacent sequences: A206325 A206326 A206327 * A206329 A206330 A206331

Keyword

nonn,easy

Author

Michel Lagneau, Feb 06 2012

Status

approved