This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.
[ p: p in PrimesUpTo(1000) | #[ x: x in ResidueClassRing(p) | x^3 eq 2 ] eq 1 ]; // Klaus Brockhaus, Apr 11 2009
Select[Prime[Range[150]],MemberQ[{0,2},Mod[#,3]]&] (* Harvey P. Dale, Jun 14 2011 *)
is(n)=isprime(n) && n%3!=1 \\ Charles R Greathouse IV, Apr 20 2015
from itertools import count, islice from sympy import isprime def A045309_gen(): # generator of terms yield from (2,3) yield from filter(isprime, count(5,6)) A045309_list = list(islice(A045309_gen(),48)) # Chai Wah Wu, Apr 28 2025
[p: p in PrimesUpTo(740)|p mod 6 in {1,2}]; // Vincenzo Librandi, Dec 18 2010
Select[Prime[Range[150]], MemberQ[{1, 2}, Mod[#, 6]] &] (* Vladimir Joseph Stephan Orlovsky, Feb 18 2012 *)
select(t -> t mod numtheory:-lambda(t) = 1, [seq(6*k+3,k=1..10^6)]); # Robert Israel, Jul 12 2015
Cases[Range[555,10^6,6],n_/;Mod[n,CarmichaelLambda[n]]==1]
Korselt(n)=my(f=factor(n)); for(i=1, #f[, 1], if(f[i, 2]>1||(n-1)%(f[i, 1]-1), return(0))); 1 is(n)=n%6==3 && Korselt(n) && n>9 \\ Charles R Greathouse IV, Jul 20 2015
a(1) = abs(3*1-1-(3*1+1/2-1/2)) = 1; a(2) = abs(3*2-1-(3*2+1/2+1/2)) = 2.
A003627 := proc(n) if n <= 2 then op(n,[2,5]) ; ; else for a from procname(n-1)+2 by 2 do if isprime(a) and (a mod 3) =2 then return a ; end if; end do: end if; end proc: A007645 := proc(n) if n <= 2 then op(n,[3,7]) ; ; else for a from procname(n-1)+2 by 2 do if isprime(a) and (a mod 3) <> 2 then return a ; end if; end do: end if; end proc: A171715 := proc(n) abs(A003627(n)-A007645(n)) ; end proc: # R. J. Mathar, Apr 24 2010
Module[{nn=500,p1,p2,len},p1=Select[3*Range[nn]-1,PrimeQ];p2=Select[Flatten[#+{0,1}&/@ (3*Range[nn])],PrimeQ];len=Min[Length[p1],Length[p2]]; Abs[#[[1]]-#[[2]]]&/@ Thread[ {Take[p1,len],Take[p2,len]}]] (* Harvey P. Dale, Aug 29 2023 *)
korselt:= proc(n) uses numtheory; local p;
if isprime(n) or not issqrfree(n) then return false fi;
for p in factorset(n) do
if n-1 mod (p-1) <> 0 then return false fi
od;
true
end proc:
select(korselt, [seq(seq(6*i+j,j=[3,5]),i=1..10^5)]); # Robert Israel, Jul 20 2015
Select[Range[100000], !PrimeQ[#] && IntegerQ[(#-1)/CarmichaelLambda[#]] && !Mod[#,6]==1&]
Korselt(n,f=factor(n))=for(i=1,#f[,1],if(f[i,2]>1||(n-1)%(f[i,1]-1),return(0)));1
list(lim)={
my(v=List(),p=2);
forstep(n=561,lim,[12,6],
if(Korselt(n),listput(v,n))
);
forprime(q=3,lim,
forstep(n=p+if(p%6<5,4,6),q-2,6,
if(Korselt(n),listput(v,n))
);
p=q
);
vecsort(Vec(v))
}; \\ Charles R Greathouse IV, Apr 25 2012
Union[6Range[42] + 3, Select[6Range[43] - 1, Not[PrimeQ[#]] &]] (* Alonso del Arte, Jun 05 2011 *)
select(n->(n%6==3 && n>3) || (n%6==5 && !isprime(n)), vector(1000,i,i)) \\ Charles R Greathouse IV, Jun 05 2011
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