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 1-3 of 3 results.

A130904 Numbers n such that the trajectory of the map n -> (n + lpf(n)) / 2 reaches 3, where lpf(n) is the least prime factor of n (A020639).

Original entry on oeis.org

3, 4, 6, 9, 10, 15, 16, 18, 25, 27, 28, 30, 33, 34, 48, 49, 51, 52, 54, 55, 57, 58, 63, 64, 66, 91, 93, 94, 96, 99, 100, 102, 105, 106, 108, 111, 112, 114, 119, 121, 123, 124, 126, 129, 130, 169, 180, 183, 184, 186, 187, 189, 190, 195, 196, 198
Offset: 1

Views

Author

Grant Garcia, Jan 06 2011

Keywords

Comments

The only prime term is 3 because all primes map to themselves.

Examples

			(15 + 3) / 2 = 9, (9 + 3) / 2 = 6, (6 + 2) / 2 = 4, and (4 + 2) / 2 = 3, thus 15 is in the sequence.
(21 + 3) / 2 = 12, (12 + 2) / 2 = 7, and (7 + 7) / 2 = 7, so 21 never reaches 3 and therefore is not in the sequence.

Crossrefs

Cf. A177980, A020639, A061228.

A179329 Number of iterations of (n + lpf(n)) / 2 required to reach a prime, where lpf equals the least prime factor.

Original entry on oeis.org

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

Views

Author

Grant Garcia, Jan 12 2011

Keywords

Comments

Zeros indicate prime indices.

Examples

			a(15) gives (15 + 3) / 2 = 9, (9 + 3) / 2 = 6, (6 + 2) / 2 = 4, (4 + 2) / 2 = 3. Four iterations were required to reach a prime, so a(15) = 4.

Crossrefs

Cf. A177980, A020639, A061228.

Programs

  • Mathematica
    f[n_] := Length@ NestWhileList[(# + FactorInteger[#][[1, 1]])/2 &, n, ! PrimeQ@ # &] - 1; Array[f, 105, 2]

A179997 Where records occur in A179329.

Original entry on oeis.org

2, 4, 6, 9, 15, 25, 48, 91, 169, 336, 669, 1335, 2665, 5317, 10573, 21037, 42072, 84141, 168279, 336553, 673099, 1345639, 2691276, 5382549, 10765095, 21528959, 43057916, 86115821, 172231631, 344463251, 688926491, 1377847349, 2755694696, 5511375473, 11022750944
Offset: 1

Views

Author

Grant Garcia, Jan 13 2011

Keywords

Comments

a(n + 1) / a(n) converges to 2.

Crossrefs

Cf. A179329, A177980, A130904, A020639, A061228.

Extensions

Corrected and extended by Grant Garcia, Jan 19 2011
a(30)-a(35) from Amiram Eldar, Oct 25 2024
Showing 1-3 of 3 results.

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

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