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.

A068507 Highly composite numbers sandwiched between twin primes.

Original entry on oeis.org

4, 6, 12, 60, 180, 240, 7560, 55440, 110880, 73329656400, 18632716502400, 130429015516800, 48519593772249600, 149602080797769600, 74377068101903920953600, 927967188666725711881005276648000, 241271469053348685089061371928480000
Offset: 1

Views

Author

Lekraj Beedassy, Mar 25 2002

Keywords

Comments

Intersection of (A072826 - 1) and (A072828 + 1). - Lekraj Beedassy, Nov 27 2003
The next term, a(18), is A002182(1002), it has 77 digits. - M. F. Hasler, Jun 23 2019
a(22) > 10^17030, if it exists. - Amiram Eldar, Dec 03 2020

Examples

			60 is between 59 and 61.

Links

Crossrefs

Cf. A002182, A072826, A072828, A117825, A321995.
This is also the intersection of A002182 and A014574.

Formula

a(n) = A002182(A321995(n)). - Amiram Eldar, Dec 03 2020

Extensions

Corrected and extended by Lior Manor, Jun 03 2002
More terms from Bill McEachen, May 24 2006
a(18)-a(20) from M. F. Hasler, Jun 23 2019

A353302 Numbers k such that A004394(k)-1 and A004394(k)+1 are twin primes.

Original entry on oeis.org

3, 4, 5, 9, 11, 12, 24, 25, 76, 82, 105, 139, 217, 1370
Offset: 1

Views

Author

Amiram Eldar, Apr 10 2022

Keywords

Comments

a(15) > 10^5, if it exists.

Examples

			3 is a term since the third superabundant number is A004394(3) = 4 and {4-1, 4+1} = {3, 5} is a twin primes pair.

Crossrefs

Intersection of A353300 and A353301.
Cf. A001097, A004394, A068507, A321995.

Programs

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

A375198 Numbers k such that A025487(k)-1 and A025487(k)+1 are twin primes.

Original entry on oeis.org

3, 4, 6, 9, 13, 15, 20, 21, 24, 29, 30, 42, 54, 56, 59, 72, 77, 83, 96, 104, 105, 109, 138, 161, 166, 174, 186, 203, 208, 221, 232, 237, 266, 270, 288, 295, 336, 338, 347, 387, 389, 395, 400, 401, 449, 468, 469, 472, 479, 506, 520, 543, 584, 617, 633, 643, 668
Offset: 1

Views

Author

Amiram Eldar, Aug 04 2024

Keywords

Links

Crossrefs

Cf. A001097, A001359, A006512, A014574, A025487, A375197.
Similar sequences: A321995, A353302.

Programs

  • Mathematica
    Position[Cases[Import["https://oeis.org/A025487/b025487.txt", "Table"], {, }][[;; , 2]], _?(PrimeQ[# - 1] && PrimeQ[# + 1] &)] // Flatten

Formula

A025487(a(n)) = A375197(n).

A328329 Lesser of twin primes p such that d(p+1) > d(q+1) for all lessers of twin primes q < p, where d(n) is the number of divisors of n (A000005).

Original entry on oeis.org

3, 5, 11, 29, 59, 179, 239, 419, 1319, 2339, 3119, 3359, 6299, 7559, 21599, 21839, 33599, 35279, 42839, 55439, 100799, 110879, 287279, 415799, 957599, 1621619, 1713599, 1867319, 1940399, 2489759, 3991679, 6652799, 11531519, 18258239, 22822799, 26732159, 28828799
Offset: 1

Views

Author

Amiram Eldar, Oct 12 2019

Keywords

Comments

The corresponding values of d(p+1) are 3, 4, 6, 8, 12, 18, 20, 24, 32, 36, 40, 48, 54, 64, 72, 80, 84, 90, 96, 120, 126, 144, 160, 192, 216, 240, 252, 256, 270, 288, 320, 384, 432, 448, 480, 512, 576, ...

Crossrefs

Cf. A000005, A001359, A068507, A321995, A326392.

Programs

  • Mathematica
    dm = DivisorSigma[0, 4]; s = {3}; Do[If[!PrimeQ[6n - 1] || !PrimeQ[6n + 1], Continue[]]; d = DivisorSigma[0, 6n]; If[d > dm, dm = d; AppendTo[s, 6n - 1]], {n, 1, 10^5}]; 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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