

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^t1)/(q1) for any primepower 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
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OFFSET

1,1


COMMENTS

The numbers in this sequence are called zetaprimes, 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), 927930.


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^n1)/(q1);
while x < 1000 do
Add(repunitList, x);
n:=n+1;
x:=(q^n1)/(q1);
od;
fi;
od;
# Remove repunits from filtered prime list to produce list of zetaprimes
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



