A071695 -id:A071695 - cp's OEIS frontend

A205171 The lesser of twin primes == 1 (mod 8).

17, 41, 137, 281, 521, 569, 617, 641, 809, 857, 881, 1049, 1289, 1481, 1697, 1721, 2081, 2129, 2657, 2729, 2801, 2969, 3257, 3329, 3929, 4001, 4049, 4217, 4241, 4337, 4481, 4649, 4721, 5009, 5417, 5441, 5657, 5849, 6089, 6449, 6569, 6689, 6761, 7457

Offset: 1

Robert G. Wilson v, Jan 22 2012

Cf. A071695, A205172.

Intersection of A017077 and A001359.

Select[ Prime@ Range@ 1000, Mod[#, 8] == 1 && PrimeQ[# + 2] &]

A074381 (p-1)/2 mod 2, where p is the n-th prime for which p+2 is also prime; i.e., a(n)=0 if p==1 (mod 4), a(n)=1 if p==3 (mod 4).

Original entry on oeis.org

1, 0, 1, 0, 0, 0, 1, 1, 0, 1, 0, 0, 1, 1, 0, 1, 1, 0, 0, 1, 1, 1, 1, 0, 0, 0, 1, 0, 0, 1, 0, 0, 1, 0, 0, 1, 1, 0, 0, 1, 1, 0, 0, 0, 0, 1, 1, 1, 0, 1, 1, 1, 1, 0, 0, 1, 1, 0, 1, 0, 0, 1, 0, 1, 1, 0, 0, 0, 1, 0, 1, 0, 0, 1, 0, 1, 1, 0, 0, 0, 0, 1, 1, 1, 1, 0, 1, 0, 1, 1, 0, 0, 1, 1, 1, 0, 0, 1, 1, 0, 1, 0, 0, 0, 1

Offset: 1

Roger L. Bagula, Sep 24 2002

Cf. A001359, A071695, A071698.

Mod[(Select[Prime/@Range[600], PrimeQ[ #+2]&]-1)/2, 2]

Edited by Dean Hickerson and Robert G. Wilson v, Oct 09 2002

A074396 a(n) = 10 - (p mod 10), where p is the n-th prime congruent to 1 (mod 4) for which p+2 is also prime.

Original entry on oeis.org

5, 3, 1, 9, 9, 3, 1, 3, 1, 9, 9, 9, 1, 3, 9, 1, 9, 3, 9, 1, 9, 1, 3, 1, 9, 9, 3, 9, 3, 1, 3, 9, 1, 9, 3, 1, 9, 1, 3, 1, 1, 9, 1, 3, 1, 1, 9, 3, 9, 9, 3, 1, 9, 1, 3, 3, 1, 9, 3, 9, 9, 3, 3, 1, 9, 1, 9, 3, 9, 3, 9, 3, 9, 1, 1, 3, 1, 1, 1, 1, 9, 9, 1, 1, 3, 1, 3, 3, 1, 1, 1, 3, 3, 3, 9, 1, 9, 9, 9, 3, 9, 1, 3, 3, 1

Offset: 1

Roger L. Bagula, Sep 24 2002

nonn

			The first 5 such primes are 5, 17, 29, 41, 101. For these, 10 - (p mod 10) is 5, 3, 1, 9, 9.

Cf. A071695.

10-Mod[ #, 10]&/@Select[Prime/@Range[1500], PrimeQ[ #+2]&&Mod[ #, 4]==1&]

Edited by Dean Hickerson, Oct 09 2002

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

Original entry on oeis.org

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

James S. DeArmon, Jan 01 2025

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.

			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.

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

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

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

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

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A205171 The lesser of twin primes == 1 (mod 8).

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A074381 (p-1)/2 mod 2, where p is the n-th prime for which p+2 is also prime; i.e., a(n)=0 if p==1 (mod 4), a(n)=1 if p==3 (mod 4).

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A074396 a(n) = 10 - (p mod 10), where p is the n-th prime congruent to 1 (mod 4) for which p+2 is also prime.

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

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