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

1,1

Comments

For pairs of cousin primes (p,p+4) such that p == 9 (mod 10) and pairs of cousin primes (p,p+4) such that p == 7 (mod 10), see A074822 and A289353, respectively. A074822, A289353 and this sequence give all the lesser members p of pairs of cousin primes.

Links

Charles R Greathouse IV, Table of n, a(n) for n = 1..10000

Example

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).

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 *)

Prog

(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]));
(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

Crossrefs

Cf. A023200, A074822, A001223, A001359, A046132, A160440, A289353.

Sequence in context: A138249 A181604 A084476 * A247584 A049173 A049156

Adjacent sequences: A289410 A289411 A289412 * A289414 A289415 A289416

Keyword

nonn

Author

Muniru A Asiru, Jul 06 2017

Status

approved