login
The OEIS Foundation is supported by donations from users of the OEIS and by a grant from the Simons Foundation.

 

Logo


Hints
(Greetings from The On-Line Encyclopedia of Integer Sequences!)
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

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

Lookup | Welcome | Wiki | Register | Music | Plot 2 | Demos | Index | Browse | More | WebCam
Contribute new seq. or comment | Format | Style Sheet | Transforms | Superseeker | Recent
The OEIS Community | Maintained by The OEIS Foundation Inc.

License Agreements, Terms of Use, Privacy Policy. .

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