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A286319
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Prime p such that p^2-p-1 or p^2+p-1 is the smallest prime of a twin prime pair.
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1
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2, 3, 5, 7, 41, 59, 67, 89, 101, 131, 139, 379, 457, 743, 761, 1193, 1201, 1381, 1549, 1567, 1747, 1789, 2137, 2411, 2557, 2647, 2663, 2729, 2731, 3011, 3221, 3251, 3449, 4057, 4159, 4447, 4561, 4751, 5179, 5641, 6173, 6397, 6599, 6833, 7229, 8669, 9059, 9157, 9323
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OFFSET
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1,1
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COMMENTS
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Union of A088483 and A120364.
3 is the only prime such that p^2-p-1 and p^2+p-1 are both the smallest of a prime twin pair.
For prime p > 3 if p+1 is divisible by 6 then the smallest prime of the prime twin pair is p^2+p-1 and p^2-p-1 if not.
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LINKS
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Pierre CAMI, Table of n, a(n) for n = 1..50000
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EXAMPLE
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2^2+2-1=5 and (5,7) is a twin prime pair so a(1)=2.
3^2-3-1=5, 3^2+3-1=11 and (5,7), (11,13) are twin prime pairs so a(2)=3.
5^2+5-1=29 and (29,31) is a twin prime pair so a(3)=5.
7^2-7-1=41 and (41,43) is a twin prime pair so a(4)=7.
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MATHEMATICA
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sptppQ[n_]:=AllTrue[{n^2-n-1, n^2-n+1}, PrimeQ]||AllTrue[{n^2+n-1, n^2+ n+ 1}, PrimeQ]; Select[Prime[Range[1200]], sptppQ] (* The program uses the AllTrue function from Mathematica version 10 *) (* Harvey P. Dale, May 04 2019 *)
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CROSSREFS
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Cf. A001359, A088483, A088485, A120364.
Sequence in context: A235395 A090714 A048400 * A090716 A083820 A244556
Adjacent sequences: A286316 A286317 A286318 * A286320 A286321 A286322
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KEYWORD
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nonn
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AUTHOR
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Pierre CAMI, May 11 2017
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STATUS
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approved
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