A379750 First prime of cousin prime pairs which differ, in their binary representation, by a single bit.

3, 19, 43, 67, 97, 163, 193, 307, 313, 379, 457, 499, 643, 673, 739, 769, 859, 883, 907, 937, 1009, 1297, 1483, 1489, 1579, 1609, 1867, 1873, 1993, 2083, 2137, 2203, 2347, 2377, 2473, 2539, 2617, 2659, 2683, 2689, 2707, 2833, 2857, 2953, 3019, 3163, 3187, 3217

Offset

1,1

Comments

The first prime of a cousin prime pair is a prime p for which p+4 is also prime.

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.

Links

Table of n, a(n) for n=1..48.

Example

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.
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.

Mathematica

Select[Prime[Range[480]], PrimeQ[#+4]&&Mod[#, 8]<4&] (* James C. McMahon, Mar 01 2025 *)

Prog

(Python)
import sympy
def ok(n): return (n&5)==1 and sympy.isprime(n) and sympy.isprime(n+4)

Crossrefs

Cf. A023200 (cousin primes), A047471, A071695.

Sequence in context: A042371 A141644 A141170 * A107154 A141373 A336792

Adjacent sequences: A379747 A379748 A379749 * A379751 A379752 A379753

Keyword

nonn,base,new

Author

James S. DeArmon, Jan 01 2025

Extensions

a(45)-a(48) from James C. McMahon, Mar 01 2025

Status

approved