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A206328
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Primes of the form n^2+1 such that (n+2)^2+1 is also prime.
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8
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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
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OFFSET
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1,1
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COMMENTS
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For n > 1, a(n) ==7 (mod 10) because n ==4 (mod 10).
Conjecture: this sequence is infinite.
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LINKS
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EXAMPLE
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For n = 4, n^2 + 1 = 17 is prime and (n+2)^2 + 1 = 37 is also prime => 17 is in the sequence.
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MAPLE
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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:
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MATHEMATICA
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Select[Partition[Range[3000]^2+1, 3, 1], AllTrue[{#[[1]], #[[3]]}, PrimeQ]&][[All, 1]] (* Harvey P. Dale, Jan 16 2023 *)
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CROSSREFS
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KEYWORD
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nonn,easy
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AUTHOR
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STATUS
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approved
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