cp's OEIS Frontend

This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.

Showing 1-4 of 4 results.

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).

Original entry on oeis.org

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

Views

Author

Reinhard Zumkeller, Jul 08 2002

Keywords

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

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).

Original entry on oeis.org

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

Views

Author

Reinhard Zumkeller, Jul 08 2002

Keywords

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

A072745 Product of the members of pairs of primes (p, q) with p < q and such that, for some integer k, (p+q)/2 = 2^k and p > 2^(k-1).

Original entry on oeis.org

15, 55, 247, 799, 943, 4087, 14359, 14863, 15943, 51847, 56887, 59911, 62287, 64807, 65311, 200143, 208783, 234919, 245503, 255583, 259543, 260119, 262063, 848767, 869647, 884551, 960367, 974047, 977287, 983551, 1003207, 1026967
Offset: 1

Views

Author

Reinhard Zumkeller, Jul 08 2002

Keywords

Crossrefs

Cf. A072742, A072743, A072744.

Programs

  • PARI
    listkp(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 = listkp(i)); if (#klist, for (j=1, #klist, listput(list, klist[j])));); Vec(list);}
upto(11) \\ Michel Marcus, Jan 22 2022

Formula

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

Extensions

Name edited by Michel Marcus, Jan 22 2022

A072746 Number of pairs of primes (p, q) such that, for some integer k, (p+q)/2 = 2^k, 2^(k-1) < p < q, and p <= n.

Original entry on oeis.org

0, 0, 1, 1, 2, 2, 2, 2, 2, 2, 2, 2, 3, 3, 3, 3, 4, 4, 4, 4, 4, 4, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 7, 7, 7, 7, 7, 7, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8
Offset: 1

Views

Author

Reinhard Zumkeller, Jul 08 2002

Keywords

Crossrefs

Cf. A072742, A072743, A071538.

Extensions

Name corrected by Jon E. Schoenfield, Jun 30 2021
Showing 1-4 of 4 results.

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