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A206328
Primes of the form n^2+1 such that (n+2)^2+1 is also prime.
8
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
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
Sequence in context: A164740 A053678 A090645 * A096407 A216428 A062230
KEYWORD
nonn,easy
AUTHOR
Michel Lagneau, Feb 06 2012
STATUS
approved