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%I #7 Dec 29 2023 10:29:58
%S 2,3,7,13,17,19,23,29,31,41,43,59,61,67,73,83,101,103,107,109,113,127,
%T 163,167,179,193,199,223,233,239,241,257,281,307,311,353,373,401,409,
%U 419,443,449,461,463,487,491,499,523,541,547,569,599,607,613,659,661,677,701,709
%N Primes of the form j-(p(j+3)-p(j))/(p(j+2)-p(j+1)), where p(j)=j-th prime.
%C Primes of the form j-A031165(j)/A001223(j+1). In cases like j=28 and j=32 which create the same prime (here: 23), the prime is only listed once.
%e If j=12, then 12-(p(12+3)-p(12))/(p(12+2)-p(12+1))=12-(47-37)/(43-41)=7=a(3).
%e If j=48, then 48-(p(48+3)-p(48))/(p(48+2)-p(48+1))=48-(233-223)/(229-227)=43: prime, in the sequence.
%e If j=88, then 88-(p(88+3)-p(88))/(p(88+2)-p(88+1))=88-(467-457)/(463-461)=83: prime, in the sequence
%t Select[Table[n-(Prime[n+3]-Prime[n])/(Prime[n+2]-Prime[n+1]),{n,1000}],PrimeQ[ #] &&#>0&]//Union (* _Harvey P. Dale_, Aug 12 2020 *)
%Y Cf. A000040.
%K nonn,less
%O 1,1
%A _Juri-Stepan Gerasimov_, Sep 10 2008
%E Corrected definition and examples, added many more terms - _R. J. Mathar_, Sep 13 2008
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