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Number of other odd numbers between the twin primes, with a(1) = 1.
0

%I #18 Jun 20 2015 14:52:36

%S 1,1,1,4,4,7,4,13,1,13,4,13,4,1,13,4,13,4,13,16,34,4,13,28,22,13,7,10,

%T 7,73,4,1,13,10,67,4,7,4,13,28,37,22,4,4,7,52,10,13,1,58,4,22,13,10,

%U 31,40,1,25,7,22,13,25,1,10,7,4,46,13,19,13,19,82,19,31,13,10,7,28,4,82,13,58,22,40,1,19,13,13,4,7,34,1

%N Number of other odd numbers between the twin primes, with a(1) = 1.

%C Bisection of A256262.

%F a(n) = abs((A001359(n+1) - A001359(n))/2 - 2).

%F a(n) = abs((A006512(n+1) - A006512(n))/2 - 2).

%e --------------------------------------------

%e . Other Twin

%e . odd numbers primes

%e n A255763 A001097 a(n)

%e --------------------------------------------

%e 1 1 3, 5, 7 1

%e 2 9 11, 13 1

%e 3 15 17, 19 1

%e 4 21, 23, 25, 27 29, 31 4

%e 5 33, 35, 37, 39 41, 43 4

%e ...

%e For n = 5, between the successive pairs of twin primes [29, 31] and [41, 43] there are four odd numbers that are not twin primes: 33, 35, 37, 39, so a(5) = 4.

%Y Cf. A001359, A001097, A006512, A255763, A256262.

%K nonn

%O 1,4

%A _Omar E. Pol_, Jun 15 2015