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Search: id:A058264
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| A058264 |
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Smallest prime p of two consecutive primes, p < q, such that GCD( p-1, q-1 ) = 2n. |
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1
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| 3, 13, 31, 89, 181, 661, 113, 2113, 523, 13421, 2311, 4177, 35543, 39901, 4831, 44417, 1327, 12853, 119321, 52321, 82657, 36389, 136897, 203713, 95651, 59281, 255259, 178697, 531919, 427621, 2640581, 1414849, 643303, 3021173, 175141
(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 GCD( p-1, q-1 ) must be even.
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EXAMPLE
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n = 49: a(49) = 604073 because GCD[604073-1,604171-1] = GCD[6164.98,6165.98] = 98 = 2n. For n = 4, a(4) = 89 because GCD[89-1,97-1] = GCD[8.11,8.16] = 8 = 2n and these primes are the smallest with this property.
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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}]; a
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CROSSREFS
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Cf. A006093, A067605.
Sequence in context: A106090 A067980 A007686 this_sequence A034050 A107689 A073337
Adjacent sequences: A058261 A058262 A058263 this_sequence A058265 A058266 A058267
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KEYWORD
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nonn
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AUTHOR
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Labos E. (labos(AT)ana.sote.hu), Dec 06 2000
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EXTENSIONS
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Edited by Robert G. Wilson v (rgwv(AT)rgwv.com), Feb 01 2002
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