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A117675 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). 0
9, 11, 13, 20, 23, 29, 47, 64, 70, 88, 121, 126, 145, 148, 153, 174, 190, 195 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,1

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)

LINKS

Table of n, a(n) for n=0..17.

FORMULA

a(n) = A072225[n]:{Prime[n]} Intersection m:{Prime[m]}

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]

CROSSREFS

Cf. A019756, A072225.

Sequence in context: A289697 A104296 A254936 * A027726 A044873 A341080

Adjacent sequences:  A117672 A117673 A117674 * A117676 A117677 A117678

KEYWORD

nonn,uned

AUTHOR

Roger L. Bagula, Apr 12 2006

STATUS

approved

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Last modified June 21 00:55 EDT 2021. Contains 345329 sequences. (Running on oeis4.)