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).

9, 11, 13, 20, 23, 29, 47, 64, 70, 88, 121, 126, 145, 148, 153, 174, 190, 195

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