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Recurring numbers in the count of consecutive composite numbers between balanced primes and their lower or upper prime neighbors.
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%I #30 Jun 25 2022 10:01:58

%S 1,5,11,17,23,29,35,41,47,53,59,65,71,77,83,89,95,101,107,113,119,125,

%T 131,137,143,149,155,161,167,173,179,185,191,197,203,209,215,221,227,

%U 233,239,245,251,257,263,269,275,281,287,293,299,305,311,317,323,329

%N Recurring numbers in the count of consecutive composite numbers between balanced primes and their lower or upper prime neighbors.

%C Except for the initial term, these numbers appear to differ by 6. Proof?

%C Numbers that occur in A101597. - _David Wasserman_, Mar 26 2008

%F If the numbers continue to differ by 6, then this is the sum of paired terms of 3n+1: (1, 4, 7, 10, 13, ...); and binomial transform of [1, 4, 2, -2, 2, -2, 2, ...]. - _Gary W. Adamson_, Sep 13 2007

%F a(n) = nextprime(A054342(n)+1)-A054342(n)-1. - _David Wasserman_, Mar 26 2008

%Y Cf. A016969, A054342, A101597.

%Y Conjectured partial sums of A329502.

%K nonn

%O 2,2

%A _Cino Hilliard_, Jan 26 2005

%E More terms from _David Wasserman_, Mar 26 2008