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A117675
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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 relicating sequence).
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0
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9, 11, 13, 20, 23, 29, 47, 64, 70, 88, 121, 126, 145, 148, 153, 174, 190, 195
(list; graph; refs; listen; history; internal format)
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OFFSET
| 0,1
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COMMENTS
| 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 )
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FORMULA
| a(n) = A072225[n]:{Prime[n]} Intersection m:{Prime[m]}
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MATHEMATICA
| 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]
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CROSSREFS
| Cf. A019756, A072225.
Sequence in context: A155877 A120177 A104296 * A027726 A044873 A183980
Adjacent sequences: A117672 A117673 A117674 * A117676 A117677 A117678
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KEYWORD
| nonn,uned
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AUTHOR
| Roger L. Bagula (rlbagulatftn(AT)yahoo.com), Apr 12 2006
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