A072743 Greater members of a pair of primes (p, q) such that, for some integer k, (p+q)/2 = 2^k and p > 2^(k-1).

5, 11, 19, 47, 41, 67, 173, 167, 149, 373, 349, 331, 313, 283, 271, 761, 743, 677, 641, 593, 563, 557, 521, 1471, 1447, 1429, 1321, 1297, 1291, 1279, 1237, 1171, 1129, 1051, 1039, 2999, 2909, 2903, 2879, 2837, 2819, 2789, 2777, 2729, 2687, 2663, 2657

Offset: 1

Author

Reinhard Zumkeller, Jul 08 2002

Keywords

• nonn

Comments

For each term q=a(n), the corresponding lesser member is p=A072742(n). (Terms in this sequence are not listed in ascending order; rather, the corresponding primes p in A072742 are listed in ascending order.)

Crossrefs

Cf. A072742 (corresponding lesser members), A072746, A072744, A072745.

Programs

PARI

listkq(k) = {my(list = List()); forprime(p=2^(k-1)+1, 2^k, my(q=2^(k+1)-p); if ((q>p) && isprime(q), listput(list, q)); ); Vec(list);}
upto(k) = {my(list = List()); for (i=1, k, my(klist = listkq(i)); if (#klist, for (j=1, #klist, listput(list, klist[j])));); Vec(list);}
upto(11) \\ Michel Marcus, Jan 22 2022

Extensions

Name corrected by Jon E. Schoenfield, Jun 30 2021