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A082892 Floor(q(j)), where q(j) = 2j/log(A000230(j)); log is natural logarithm, 2j-s are prime gaps > 1, A000230(j) is the minimal lesser prime opening the consecutive prime distance equals 2j. 1

%I

%S 1,2,1,1,2,2,2,2,2,2,3,3,3,3,3,3,4,3,3,4,4,4,4,4,4,5,5,4,5,5,5,5,5,5,

%T 5,6,5,6,6,6,6,6,7,6,6,6,6,7,7,7,7,7,7,7,7,8,8,7,8,8,8,7,8,8,8,9,8,8,

%U 9,8,8,8,9,10,9,9,10,9,8,9,9,9,9,9,9,9,9,10,10,10,10,10,9,10,10,10,10,10,11

%N Floor(q(j)), where q(j) = 2j/log(A000230(j)); log is natural logarithm, 2j-s are prime gaps > 1, A000230(j) is the minimal lesser prime opening the consecutive prime distance equals 2j.

%C For these larger and larger gap-initiating primes, integer part of relevant quotient,q, may exceed 27, all values between 1 and 28 occur. Observation supports conjecture that infsup(q) is infinity.

%t t=A000230 list; Table[Floor[2*j/Log[Part[t,j]]//N],{j,1,Length[t]}]

%Y Cf. A000230, A082862, A082884-A082891, A002386.

%K nonn

%O 1,2

%A _Labos Elemer_, Apr 17 2003

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