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A114792
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a(n) = ((p(n+1)-p(n+2))/2)-th integer among those positive integers not occurring earlier in the sequence, where p(n) is the n-th prime.
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1
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1, 2, 4, 3, 6, 5, 8, 10, 7, 12, 11, 9, 14, 16, 17, 13, 19, 18, 15, 22, 21, 24, 26, 23, 20, 27, 25, 29, 35, 30, 32, 28, 37, 31, 36, 38, 34, 40, 41, 33, 45, 39, 43, 42, 50, 51, 46, 44, 48, 52, 47, 56, 54, 55, 57, 49, 59, 58, 53, 64, 67, 61, 60, 63, 71, 66, 70, 62, 68, 72, 74, 73
(list; graph; refs; listen; history; internal format)
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OFFSET
| 1,2
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COMMENTS
| Sequence is a permutation of the positive integers if and only if there are an infinite number of twin primes pairs.
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EXAMPLE
| a(1)=1 by definition. a(2)=2 since (p(4)-p(3))/2=(7-5)/2=1 and the first integer not appearing in the sequence so far is 2.
a(3)=4 since (p(5)-p(4))/2=(11-7)/2=2 and the second integer not appearing in the sequence is 4.
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MATHEMATICA
| f[n_] := Block[{c = (Prime[n + 2] - Prime[n + 1])/2, d = 0, k = 1}, While[d < c, k++; If[ ! MemberQ[lst, k], d++ ]]; AppendTo[lst, k]]; lst = {1}; Do[ f[n], {n, 2, 72}]; lst (* Robert G. Wilson v *)
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CROSSREFS
| Cf. A028334, inverse at A119618.
Sequence in context: A114112 A113981 A143692 * A113324 A143691 A129767
Adjacent sequences: A114789 A114790 A114791 * A114793 A114794 A114795
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KEYWORD
| nonn
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AUTHOR
| Leroy Quet Jun 02 2006
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EXTENSIONS
| More terms from Robert G. Wilson v (rgwv(at)rgwv.com), Jun 07 2006
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