

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 multireplication 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



