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.

A072828 Primes p such that p+1 is a highly composite number.

Original entry on oeis.org

3, 5, 11, 23, 47, 59, 179, 239, 359, 719, 839, 1259, 5039, 7559, 10079, 55439, 110879, 166319, 665279, 1081079, 1441439, 6486479, 32432399, 61261199, 698377679, 735134399, 1102701599, 1396755359, 2205403199, 20951330399, 41902660799
Offset: 1

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Author

Shyam Sunder Gupta, Jul 21 2002

Keywords

Examples

			47 is a term because it is prime and also 47+1=48 is a highly composite number.

Links

Crossrefs

Cf. A002182, A068507, A072826, A214873, A306588.

Formula

a(n) == 2 (mod 3) for n > 1 (because highly composite numbers > 4 are == 0 (mod 3); see A002182). - Jonathan Sondow, Nov 05 2015
a(n) = A002182(A306588(n)) - 1. - Amiram Eldar, Dec 03 2020

A306587 Numbers k such that A002182(k)+1 is prime.

Original entry on oeis.org

1, 2, 3, 4, 5, 7, 9, 11, 12, 18, 20, 22, 23, 26, 28, 30, 34, 35, 44, 49, 54, 57, 60, 63, 74, 78, 84, 91, 97, 102, 104, 108, 111, 112, 114, 116, 118, 126, 134, 143, 145, 149, 159, 162, 167, 173, 177, 179, 188, 204, 208, 214, 230, 236, 238, 247, 249, 280, 294, 298
Offset: 1

Views

Author

Dmitry Kamenetsky, Mar 02 2019

Keywords

Links

Crossrefs

Cf. A002182 (highly composite numbers), A072828, A306588.

Extensions

More terms from Daniel Suteu, Mar 02 2019

A321995 Indices of highly composite numbers A002182 which are between a twin prime pair.

Original entry on oeis.org

3, 4, 5, 9, 11, 12, 20, 28, 30, 84, 108, 118, 143, 149, 208, 330, 362, 1002, 2395, 3160, 10535
Offset: 1

Views

Author

M. F. Hasler, Jun 23 2019

Keywords

Comments

The highly composite numbers are listed in A068507, but their growth is such that one cannot list the terms beyond A002182(362), corresponding to a(17), in the DATA section.
The term a(21) corresponds to A002182(10535) = A108951(52900585920). - Daniel Suteu, Jun 27 2019
a(22) > 779674, if it exists. - Amiram Eldar, Dec 03 2020

Crossrefs

Cf. A068507, A002182, A002822.

Programs

  • PARI
    select( x->ispseudoprime(x-1)&&ispseudoprime(x+1), A2182, 1) \\ assuming A2182 holds enough terms of A002182. - M. F. Hasler, Jun 23 2019

Formula

Intersection of A306587 and A306588. - Daniel Suteu, Jun 27 2019

Extensions

a(21) from Daniel Suteu, Jun 27 2019 (obtained from A. Flammenkamp's data)

A353300 Numbers k such that A004394(k)-1 is prime.

Original entry on oeis.org

3, 4, 5, 6, 8, 9, 11, 12, 13, 14, 15, 16, 19, 20, 24, 25, 26, 30, 32, 41, 47, 48, 49, 51, 57, 59, 76, 82, 83, 92, 104, 105, 117, 119, 131, 134, 137, 139, 143, 154, 166, 170, 172, 180, 209, 214, 215, 216, 217, 227, 231, 234, 247, 265, 269, 271, 284, 317, 327, 348
Offset: 1

Views

Author

Amiram Eldar, Apr 10 2022

Keywords

Comments

First differs from A306588 at n=15.

Examples

			3 is a term since A004394(3)-1 = 4-1 = 3 is prime.

Links

Crossrefs

Cf. A004394, A072826, A306588, A353301, A353302.

Programs

  • Mathematica
    s = {}; abm = 0; k = 0; Do[ab = DivisorSigma[-1, n]; If[ab > abm, abm = ab; k++; If[PrimeQ[n - 1], AppendTo[s, k]]], {n, 1, 10^6}]; s
Showing 1-4 of 4 results.

Started in 1964 by Neil J. A. Sloane | Maintained by The OEIS Foundation Inc.

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