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).

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

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

Table of n, a(n) for n=1..43.

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