|
%I #19 Aug 22 2019 10:50:12
%S 3,13,43,103,163,193,223,313,463,613,643,673,823,853,883,1093,1213,
%T 1303,1423,1483,1663,1693,1783,1873,1993,2083,2203,2293,2473,2683,
%U 2833,2953,3163,3253,3343,3463,3613,3673,3793,3943,4003,4153,4513,4783,4813,4933,5233,5413,5503,5653,5923
%N Primes p such that (p,p+4) is a pair of cousin primes and p == 3 (mod 10).
%C 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.
%H Charles R Greathouse IV, <a href="/A289413/b289413.txt">Table of n, a(n) for n = 1..10000</a>
%e For p = 193, the pair of cousin primes is (193, 197) and 193 == 3 (mod 10).
%e 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).
%p 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;
%p # Alternative:
%p select(t -> isprime(t) and isprime(t+4), [seq(i,i=3..10000, 10)]); # _Robert Israel_, Aug 02 2017
%t Select[Prime[Range[800]],Mod[#,10]==3&&PrimeQ[#+4]&] (* _Harvey P. Dale_, Aug 22 2019 *)
%o (GAP)
%o P:=Filtered([1..10000],IsPrime);;
%o 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]));
%o (PARI) isok(p) = isprime(p) && isprime(p+4) && (p%10==3); \\ _Michel Marcus_, Jul 19 2017
%o (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
%Y Cf. A023200, A074822, A001223, A001359, A046132, A160440, A289353.
%K nonn
%O 1,1
%A _Muniru A Asiru_, Jul 06 2017
|
