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%I #6 Jul 10 2019 18:43:00
%S 9,11,13,20,23,29,47,64,70,88,121,126,145,148,153,174,190,195
%N Primes indices both at the end and beginning of sequences of primes where consecutive Goldbach primes produce a fourth prime Prime(n)+Prime(n+1)+Prime(n+2) = Prime(m): A072225: replicating prime sequences of length more than one (index both at the end and beginning of a replicating sequence).
%C Replicating condition (different from a group A (operation) B=C): A, B, C consecutive in the set produce D also in the set by addition. Example of a multi-replication 5+7+11=23 23+29+31=83 83+89+97=269 5->23->83->269 (sequence not in OEIS) Similarly: 7->31->109->349->1061 (A109756)
%F a(n) = A072225[n]:{Prime[n]} Intersection m:{Prime[m]}
%t b = Flatten[Table[If[PrimeQ[Prime[n] + Prime[n + 1] + Prime[n + 2]] == True, If [Prime[n] + Prime[n + 1] + Prime[n + 2] - Prime[m] == 0, n, {}], {}], {n, 1, 200}, {m, 1, 2000}]] c = Flatten[Table[If[PrimeQ[Prime[n] + Prime[n + 1] + Prime[n + 2]] == True, If [Prime[n] + Prime[n + 1] + Prime[n + 2] - Prime[m] == 0, m, {}], {}], {n, 1, 200}, {m, 1, 2000}]] Output[n]=Intersection[c, b]
%Y Cf. A019756, A072225.
%K nonn,uned
%O 0,1
%A _Roger L. Bagula_, Apr 12 2006
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