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 A270123 Primes p such that p is equivalent to 3 modulo 4, p is neither 11 nor 23, and p is not a generalized repunit prime (i.e., p cannot be written as (q^t-1)/(q-1) for any prime-power q). 0
 19, 43, 47, 59, 67, 71, 79, 83, 103, 107, 131, 139, 151, 163, 167, 179, 191, 199, 211, 223, 227, 239, 251, 263, 271, 283, 311, 331, 347, 359, 367, 379, 383, 419, 431, 439, 443, 463, 467, 479, 487, 491, 499 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,1 COMMENTS The numbers in this sequence are called zeta-primes, and they exactly identify when (for n > 4) the set of maximal subgroups of even order fail to cover Alt(n). This is proved in the reference below. LINKS B. J. Benesh, D. C. Ernst, and N. Sieben Impartial avoidance and achievement games for generating symmetric and alternating groups, arXiv:1508.03419 [math.CO], 2015. H. Dubner, Generalized repunit primes, Math. Comp., 61 (1993), 927-930. PROG (GAP) # Primes is a list of the 168 primes below 1000. primeList:=[]; primeList:=ShallowCopy(Primes); # Remove {3} and {11, 23}, which are in the 2nd, 5th, and 9th positions, respectively. Remove(primeList, 9); Remove(primeList, 5); Remove(primeList, 2); # Remove anything that is not 3 mod 4. primeList:=Filtered(primeList, p->p mod 4 = 3); # This generates all repunits so that we may remove them from the list of primes. repunitList:=[]; for q in [2..1000] do if IsPrimePowerInt(q) then n:=1; x:=(q^n-1)/(q-1); while  x < 1000 do Add(repunitList, x); n:=n+1; x:=(q^n-1)/(q-1); od; fi; od; # Remove repunits from filtered prime list to produce list of zeta-primes getZeta:=function() local zlist, p; zlist:=[]; for p in primeList do if not p in repunitList then Add(zlist, p); fi; od; return zlist; end; CROSSREFS Subsequence of A002145, A028491 gives examples of generalized repunit primes. Sequence in context: A156897 A094841 A001986 * A139811 A095101 A162856 Adjacent sequences:  A270120 A270121 A270122 * A270124 A270125 A270126 KEYWORD nonn AUTHOR Bret Benesh, Mar 11 2016 STATUS approved

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Last modified April 18 18:55 EDT 2021. Contains 343089 sequences. (Running on oeis4.)