A289413 Primes p such that (p,p+4) is a pair of cousin primes and p == 3 (mod 10).
3, 13, 43, 103, 163, 193, 223, 313, 463, 613, 643, 673, 823, 853, 883, 1093, 1213, 1303, 1423, 1483, 1663, 1693, 1783, 1873, 1993, 2083, 2203, 2293, 2473, 2683, 2833, 2953, 3163, 3253, 3343, 3463, 3613, 3673, 3793, 3943, 4003, 4153, 4513, 4783, 4813, 4933, 5233, 5413, 5503, 5653, 5923
Offset: 1
Keywords
Examples
For p = 193, the pair of cousin primes is (193, 197) and 193 == 3 (mod 10). Although, the primes 3 and 7 are not consecutive primes, p = 3 yields the pair of cousin primes (3, 7) and 3 == 3 (mod 10).
Links
- Charles R Greathouse IV, Table of n, a(n) for n = 1..10000
Programs
-
GAP
P:=Filtered([1..10000],IsPrime);; P1:=Concatenation([3],List(Filtered(Filtered(List([1..Length(P)-1],n->[P[n],P[n+1]]),i->i[2]-i[1]=4),j->j[1] mod 10 = 3),k->k[1]));
-
Maple
A289413:={}: for i from 1 to 1500 do if isprime(ithprime(i) + 4) and ithprime(i) mod 10 = 3 then A289413:={op(A289413), ithprime(i)}: fi: od: A289413; # Alternative: select(t -> isprime(t) and isprime(t+4), [seq(i,i=3..10000, 10)]); # Robert Israel, Aug 02 2017
-
Mathematica
Select[Prime[Range[800]],Mod[#,10]==3&&PrimeQ[#+4]&] (* Harvey P. Dale, Aug 22 2019 *)
-
PARI
isok(p) = isprime(p) && isprime(p+4) && (p%10==3); \\ Michel Marcus, Jul 19 2017
-
PARI
list(lim)=my(v=List([3]),p=13); forprime(q=17,lim+4, if(q-p==4 && p%10==3, listput(v,p)); p=q); Vec(v) \\ Charles R Greathouse IV, Aug 03 2017
Comments