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Search: id:A067604
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| A067604 |
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Smallest prime p of two consecutive primes, p < q, such that the GCD( p+1, q+1 ) = 2n. |
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+0
6
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| 3, 7, 23, 359, 139, 467, 293, 3391, 1259, 17519, 3739, 7079, 12011, 52639, 18869, 66239, 77383, 27143, 51071, 76039, 119447, 76163, 91033, 226943, 206699, 894451, 327347, 492911, 399793, 195599, 313409, 981823, 829883, 1169939, 302329
(list; graph; listen)
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OFFSET
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1,1
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COMMENT
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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
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a(1) = 3, the 3rd prime being the first entry in A066940, a(2) = 7, the 4th prime being the first entry in A066941, a(3) = 23, the 9th prime being of the first entry in A066942, a(4) = 359, the 72rd prime being the first entry in A066943, a(5) = 139, the 34th prime being the first entry in A066944.
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MATHEMATICA
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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}]; Prime[a]
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CROSSREFS
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Cf. A066940, A066941, A066942, A066944 & A067603.
Sequence in context: A060235 A090188 A001773 this_sequence A090118 A099183 A110864
Adjacent sequences: A067601 A067602 A067603 this_sequence A067605 A067606 A067607
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KEYWORD
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easy,nonn
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AUTHOR
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Robert G. Wilson v (rgwv(AT)rgwv.com), Jan 31 2002
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