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 base-three 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(q-p==r-q, print1(p", "q", "r", ")); p=q; q=r) \\ Charles R Greathouse IV, Dec 17 2016
CROSSREFS
KEYWORD
nonn,uned
AUTHOR
Roger L. Bagula, Apr 10 2006
STATUS
approved