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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

%I #10 Apr 09 2014 10:15:01

%S 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,

%T 25,29,35,30,32,28,37,31,36,38,34,40,41,33,45,39,43,42,50,51,46,44,48,

%U 52,47,56,54,55,57,49,59,58,53,64,67,61,60,63,71,66,70,62,68,72,74,73

%N 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.

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

%e 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.

%e a(3)=4 since (p(5)-p(4))/2=(11-7)/2=2 and the second integer not appearing in the sequence is 4.

%t 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_ *)

%Y Cf. A028334, inverse at A119618.

%K nonn

%O 1,2

%A _Leroy Quet_, Jun 02 2006

%E More terms from _Robert G. Wilson v_, Jun 07 2006

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Last modified March 29 07:27 EDT 2024. Contains 371265 sequences. (Running on oeis4.)