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.
%I A076746 #21 Apr 14 2025 23:42:20
%S A076746 3,7,13,17,43,47,103,107,163,167,193,197,223,227,313,317,463,467,613,
%T A076746 617,643,647,673,677,823,827,853,857,883,887,1093,1097,1213,1217,1303,
%U A076746 1307,1423,1427,1483,1487,1663,1667,1693,1697,1783,1787,1873,1877,1993
%N A076746 List giving pairs of primes of the form 10k+3 and 10k+7.
%C A076746 Except for 3 and 7, all pairs are 30k+13 and 30k+17.
%C A076746 Is this sequence infinite?
%H A076746 Roger L. Bagula, May 04 2008, <a href="/A076746/b076746.txt">Table of n, a(n) for n = 1..142</a>
%e A076746 43 and 47 are in the sequence because both are prime; 73 and 77 aren't because not both are primes.
%t A076746 a[0] = 3; a[n_] := a[n] = a[n - 1] + 10; Flatten[Table[If[PrimeQ[a[n]] && PrimeQ[a[n] + 4], {a[n],a[n] + 4}, {}], {n, 0, 1000}]] (* _Roger L. Bagula_, May 04 2008 *)
%t A076746 Flatten[Select[Table[10n+{3,7},{n,0,200}],And@@PrimeQ[#]&]] (* _Harvey P. Dale_, Dec 31 2013 *)
%o A076746 (PARI) forstep(x=3,2000,10, if(isprime(x) && isprime(x+4), print1(x, ", ", x+4, ", ")))
%o A076746 (Magma) &cat[[10*k+3, 10*k+7]: k in [0..250]| IsPrime(10*k+3) and IsPrime(10*k+7)]; // _Vincenzo Librandi_, Jun 17 2016
%Y A076746 Cf. A001097.
%Y A076746 Cf. A132243, A132242.
%K A076746 nonn
%O A076746 1,1
%A A076746 _Cino Hilliard_, Nov 11 2002
%E A076746 Edited by _Don Reble_, Jun 07 2003
%E A076746 More terms from _Roger L. Bagula_, May 04 2008