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A067603
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Least k such that the GCD( prime(k+1)+1, prime(k)+1 ) = 2n.
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6
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2, 4, 9, 72, 34, 91, 62, 478, 205, 2016, 522, 909, 1440, 5375, 2149, 6610, 7604, 2976, 5229, 7488, 11251, 7499, 8805, 20179, 18526, 70885, 28193, 40985, 33847, 17625, 27069, 77199, 66156, 90764, 26186, 141235, 70317, 856719, 110769, 50523, 217229
(list; graph; refs; listen; history; internal format)
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OFFSET
| 1,1
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COMMENTS
| Since all consecutive primes, p < q and p greater than 2, are odd, therefore the GCD( p+1, q+1 ) must be even.
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EXAMPLE
| a(1) = 2, the first entry in A066940, a(2) = 4, the first entry in A066941, a(3) = 9, the first entry in A066942, a(4) = 72, the first entry in A066943, a(5) = 34, the first entry in A066944. That is to say that the first k-th prime that has a GCD( Prime(k)+1, Prime(k+1)+1) ) of 2, 4, 6, 8, & 10 is 2, 4, 15, 72, & 34.
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MATHEMATICA
| a = Table[0, {100}]; p = 3; q = 5; Do[q = Prime[n + 1]; d = GCD[p + 1, q + 1]/2; If[d < 101 && a[[d]] == 0, a[[d]] = n]; b = c, {n, 2, 10^7}]; a
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CROSSREFS
| Cf. A066940, A066941, A066942, A066944.
Sequence in context: A162116 A162117 A162109 * A065299 A128942 A135445
Adjacent sequences: A067600 A067601 A067602 * A067604 A067605 A067606
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KEYWORD
| easy,nonn
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AUTHOR
| Robert G. Wilson v (rgwv(AT)rgwv.com), Jan 31 2002
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