A072744 Difference between the members of a pair of primes (p, q) with p < q and such that, for some integer k, (p+q)/2 = 2^k and p > 2^(k-1).

2, 6, 6, 30, 18, 6, 90, 78, 42, 234, 186, 150, 114, 54, 30, 498, 462, 330, 258, 162, 102, 90, 18, 894, 846, 810, 594, 546, 534, 510, 426, 294, 210, 54, 30, 1902, 1722, 1710, 1662, 1578, 1542, 1482, 1458, 1362, 1278, 1230, 1218, 1122, 990, 858, 822, 702, 522

Offset: 1

Author

Reinhard Zumkeller, Jul 08 2002

Keywords

• nonn

Crossrefs

Cf. A072742, A072743, A072745.

Programs

PARI

listkd(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-p));); Vec(list);}
upto(k) = {my(list = List()); for (i=1, k, my(klist = listkd(i)); if (#klist, for (j=1, #klist, listput(list, klist[j])));); Vec(list);}
upto(11) \\ Michel Marcus, Jan 22 2022

Formula

a(n) = A072743(n) - A072742(n).

Extensions

Name edited by Michel Marcus, Jan 22 2022