A072743 - OEIS

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).

%I #18 Jan 22 2022 08:42:55

%S 5,11,19,47,41,67,173,167,149,373,349,331,313,283,271,761,743,677,641,

%T 593,563,557,521,1471,1447,1429,1321,1297,1291,1279,1237,1171,1129,

%U 1051,1039,2999,2909,2903,2879,2837,2819,2789,2777,2729,2687,2663,2657

%N 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).

%C 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.)

%o (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);}

%o 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);}

%o upto(11) \\ _Michel Marcus_, Jan 22 2022

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

%K nonn

%O 1,1

%A _Reinhard Zumkeller_, Jul 08 2002

%E Name corrected by _Jon E. Schoenfield_, Jun 30 2021