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%I #9 Aug 16 2020 10:27:59
%S 0,0,0,0,3,3,0,0,0,0,0,2,1,2,1,3,0,0,0,0,0,0,0,0,0,0,0,0,0,0,2,2,3,2,
%T 7,4,7,8,8,5,0,5,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,
%U 0,0,1,0,1,2,1,2,1,1,0,1,1,0,1,2,1,2,1,4,1,2,1,3,3,4,5,1,5,4,8,0,0,0,0,0,0
%N Number of values of k for k=1,2,3,...,n-1, such that n+k divides prime(n)+prime(k), where prime(n) denotes the n-th prime.
%C Surprisingly, the nonzero terms of the sequence seem to occur in well-defined intervals separated by increasingly long intervals of zero terms, with the position of one nonzero interval located at a value of n approximately 2.4 times that of the previous one. See the link for a graph of {a(n)} vs. Log(n) to the base 2.4, for n in {1,2,...,5000}. Further,each of the integer quotients (Prime[n]+ Prime[k])/(n+k) are the same throughout each interval of nonzero values of a(n) and in fact the values of the quotients are precisely the ordinal of that interval of nonzero values.
%H John W. Layman, <a href="http://intranet.math.vt.edu/people/layman/sequences/primdif.htm">View the graph of {a(n)} vs. log(n) to the base 2.4.</a>
%e The first five primes are 2,3,5,7,11. We find that 5+1 does not divide 11+2, but 5+2 divides 11+3, 5+3 divides 11+5 and 5+4 divides 11+7. Therefore a(5)=3.
%Y Cf. A000040.
%K nonn
%O 1,5
%A _John W. Layman_, Jul 22 2005
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