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%I #9 Jun 16 2016 23:27:53
%S 1,5,7,9,13,21,29,37,41,43,47,57,69,79,85,87,91,99,113,125,133,135,
%T 139,147,161,175,185,189,191,197,211,225,239,243,245,251,263,279,293,
%U 301,303,307,317,333,349,359,363,365,373,389,407,419,425,427,433,447
%N a(n) = 2*floor((n + sin(n)/(2*sin(1/2))) * log(n)) + 1.
%C This sequence of odd integers mimics the prime numbers and more specifically it is conjectured a(n) satisfies an analog of the k-tuple conjecture (see link) with similar heuristic asymptotic formulas.
%H Benoit Cloitre, <a href="/A218851/a218851.pdf">A k-tuple conjecture for an explicit sequence</a>
%t Table[2*Floor[(n + Sin[n]/(2*Sin[1/2]))*Log[n]] + 1, {n, 60}] (* _T. D. Noe_, Nov 08 2012 *)
%o (PARI) a(n)=2*floor((n+sin(n)/2/sin(1/2))*log(n))+1
%K nonn
%O 1,2
%A _Benoit Cloitre_, Nov 07 2012