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 A379750 #48 Mar 02 2025 08:00:29
%S A379750 3,19,43,67,97,163,193,307,313,379,457,499,643,673,739,769,859,883,
%T A379750 907,937,1009,1297,1483,1489,1579,1609,1867,1873,1993,2083,2137,2203,
%U A379750 2347,2377,2473,2539,2617,2659,2683,2689,2707,2833,2857,2953,3019,3163,3187,3217
%N A379750 First prime of cousin prime pairs which differ, in their binary representation, by a single bit.
%C A379750 The first prime of a cousin prime pair is a prime p for which p+4 is also prime.
%C A379750 The only way for p and p+4 to differ at a single bit position is when p has a 0 bit at its "4" position, so p == {0,1,2,3} (mod 8), and so this sequence is the intersection of A023200 and A047471.
%e A379750 3 is a term since it's a cousin prime with 7 and their respective binary representations 011 and 111 differ at a single bit position.
%e A379750 13 is not a term since, although it's a cousin prime with 17, their respective binary representations 1101 and 10001 differ at more than a single bit position.
%t A379750 Select[Prime[Range[480]], PrimeQ[#+4]&&Mod[#,8]<4&] (* _James C. McMahon_, Mar 01 2025 *)
%o A379750 (Python)
%o A379750 import sympy
%o A379750 def ok(n): return (n&5)==1 and sympy.isprime(n) and sympy.isprime(n+4)
%Y A379750 Cf. A023200 (cousin primes), A047471, A071695.
%K A379750 nonn,base
%O A379750 1,1
%A A379750 _James S. DeArmon_, Jan 01 2025
%E A379750 a(45)-a(48) from _James C. McMahon_, Mar 01 2025