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%I #6 Sep 12 2017 18:10:09
%S 3,5,29,37,41,43,59,71,103,103,149,151,149,181,191,211,211,263,271,
%T 271,313,313,331,347,347,349,383,389,397,433,521,523,577,607,709,743,
%U 743,769,787,787,821,823,827,829,863,877,877,883,937,1039,1061,1069,1117,1129,1153
%N Primes of the form n-(p(n+2)-p(n))/(p(n+1)-p(n-1)), where p(n)=n-th prime.
%C Entries may be repeated and are shown in order of increasing generator n.
%H Harvey P. Dale, <a href="/A141578/b141578.txt">Table of n, a(n) for n = 1..1000</a>
%e n=4: 4-(13-7)/(11-5)=3=a(1).
%e n=6: 6-(19-13)/(17-11)=5=a(2).
%e n=30: 30-(131-113)/(127-109)=29=a(3).
%e n=38: 38-(173-163)/(167-157)=37=a(4).
%e n=42: 42-(193-181)/(191-179)=41=a(5).
%t With[{nn=2000},Select[#[[1]]-#[[2]]&/@(Thread[{Range[2,nn-2],(#[[4]]- #[[2]])/ (#[[3]]-#[[1]])&/@Partition[Prime[Range[nn]],4,1]}]),PrimeQ]] (* _Harvey P. Dale_, Sep 12 2017 *)
%Y Cf. A000040.
%K nonn
%O 1,1
%A _Juri-Stepan Gerasimov_, Sep 10 2008
%E Corrected and extended by _R. J. Mathar_, Sep 26 2008