

A117646


Sets of three consecutive primes with equal gaps: prime(n) + 2*m = prime(n+1) and prime(n+1) + 2*m = prime(n+2) for some m.


1



3, 5, 7, 47, 53, 59, 151, 157, 163, 167, 173, 179, 199, 211, 223, 251, 257, 263, 257, 263, 269, 367, 373, 379, 557, 563, 569, 587, 593, 599, 601, 607, 613, 647, 653, 659, 727, 733, 739, 941, 947, 953, 971, 977, 983, 1097, 1103, 1109, 1117, 1123, 1129, 1181
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OFFSET

1,1


COMMENTS

A Goedel prime equivalent to if A Implies B and B implies C then A Implies C.
In H. G. Wells's War of the Worlds, the Martians use a basethree number system: in such a system 3^n+2 instead of 2^n+1 primes would be important. Likewise instead of pairs of primes, triples of primes would be studied as "interesting", so I call these Martian Prime triples as that's what gave me the idea for finding them.
Not monotone: a(18) = 263 > 257 = a(19).  Charles R Greathouse IV, Dec 17 2016


LINKS

Harvey P. Dale, Table of n, a(n) for n = 1..1000
Wikipedia, The War of the Worlds (1953 movie)
Wikipedia, The War of the Worlds (novel)


FORMULA

a(n) = If gap=2*m then { Prime[n],Prime[n+1],Prime[n+2]}.


MATHEMATICA

a = Delete[Union[Flatten[Table[If[(Prime[n] + 2*m  Prime[n + 1] == 0) && (Prime[n + 1] + 2*m  Prime[ n + 2] == 0), {Prime[n], Prime[n + 1], Prime[ n + 2]}, {}], {m, 1, 17}, {n, 1, 200}], 1]], 1] Flatten[a]
Select[Partition[Prime[Range[200]], 3, 1], Length[Union[Differences[#]]] == 1&]// Flatten (* Harvey P. Dale, Dec 23 2018 *)


PROG

(PARI) p=2; q=3; forprime(r=5, 1e4, if(qp==rq, print1(p", "q", "r", ")); p=q; q=r) \\ Charles R Greathouse IV, Dec 17 2016


CROSSREFS

Sequence in context: A146972 A102742 A089044 * A064857 A065913 A137999
Adjacent sequences: A117643 A117644 A117645 * A117647 A117648 A117649


KEYWORD

nonn,uned


AUTHOR

Roger L. Bagula, Apr 10 2006


STATUS

approved



