A114792 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.

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

Offset

1,2

Comments

Sequence is a permutation of the positive integers if and only if there are an infinite number of twin primes pairs.

Links

Table of n, a(n) for n=1..72.

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.

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 *)

Crossrefs

Cf. A028334, inverse at A119618.

Sequence in context: A143692 A337116 A338618 * A113324 A338362 A281117

Adjacent sequences: A114789 A114790 A114791 * A114793 A114794 A114795

Keyword

nonn

Author

Leroy Quet, Jun 02 2006

Extensions

More terms from Robert G. Wilson v, Jun 07 2006

Status

approved