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 1-5 of 5 results.

A036384 Number of odd split numbers (A036382) in the interval [2^(n-1), 2^n].

Original entry on oeis.org

0, 0, 0, 0, 1, 3, 8, 18, 40, 87, 191, 400, 855, 1776, 3697, 7644, 15752, 32365, 66304, 135570, 276590, 563432, 1146045, 2328063, 4724270, 9577176, 19397428, 39256129, 79390449, 160450210, 324088695, 654261484
Offset: 1

Views

Author

Labos Elemer

Keywords

Examples

			Out of the 512 numbers with "binary order" ceiling(log_2(x)) = 10, there are 87 odd split numbers.

Crossrefs

Cf. A029827, A029837, A036378-A036390.

Extensions

Name simplified by M. F. Hasler, Apr 19 2017
a(21)-a(32) from Giovanni Resta, Apr 21 2017

A036385 Number of split numbers (A036382) with binary order (A029837) n, i.e., those in interval [ 2^(n-1), 2^n ].

Original entry on oeis.org

0, 0, 1, 3, 8, 18, 39, 81, 167, 342, 702, 1423, 2902, 5871, 11888, 24027, 48519, 97900, 197375, 397713, 800877, 1612007, 3243196, 6522366, 13112877, 26354391, 52951859, 106364992, 213608176, 428885665, 860959606
Offset: 1

Views

Author

Labos Elemer

Keywords

Examples

			Out of the 128 numbers with the binary order 8, there are 81 split numbers (odd + even); so a(7)=81.

Crossrefs

Cf. A029827, A029837, A036378-A036390.

Extensions

a(20)-a(31) from Sean A. Irvine, Oct 29 2020

A036383 First differences of odd split numbers (A036382).

Original entry on oeis.org

12, 2, 4, 26, 4, 6, 2, 10, 4, 2, 12, 24, 4, 2, 6, 2, 2, 2, 8, 4, 2, 4, 10, 2, 6, 6, 6, 8, 14, 42, 2, 4, 2, 6, 2, 4, 6, 2, 4, 4, 2, 2, 2, 2, 2, 4, 6, 4, 2, 4, 2, 2, 10, 2, 4, 6, 6, 6, 8, 4, 2, 4, 4, 14, 4, 10, 14, 8, 30, 48, 2, 2, 2, 6, 2, 4, 2, 2, 2, 2, 4, 2, 4, 2, 2, 2, 4, 2, 4, 2, 6, 2, 4, 2, 2, 2, 4, 2
Offset: 1

Views

Author

Labos Elemer

Keywords

Comments

The large local maxima are near powers of 2. Compare the differences of connected numbers (A036379).
Densities of connected (A029827) and split (A036382) numbers seem to behave in opposite way: where connected are dense, split ones are rare and vice versa.

Examples

			177, 183, 189, 195, 203, 217, 259, 261 are successive odd split numbers, so their sequence of first differences is 6, 6, 6, 8, 14, 42, 2.

Crossrefs

Cf. A029837, A036378-A036390.

A036388 Number of odd split numbers (A036382) of which the binary order (A029837) is <= n, i.e., those which occur below 2^n.

Original entry on oeis.org

0, 0, 0, 0, 1, 4, 12, 30, 70, 157, 348, 748, 1603, 3379, 7076, 14720, 30472, 62837, 129141, 264711, 541301, 1104733, 2250778, 4578841, 9303111, 18880287, 38277715, 77533844, 156924293, 317374503, 641463198, 1295724682
Offset: 1

Views

Author

Labos Elemer

Keywords

Examples

			Below 32 the only odd split number is 21, so a(5) = 1. (In this range there are also 11 primes, 7 true prime powers, 1 composite connected number (15) and 4 even split numbers.)

Crossrefs

Cf. A029837, A036378-A036390.

Formula

Partial sums of A036384. - Sean A. Irvine, Oct 29 2020

Extensions

a(9) onward corrected and a(21)-a(32) from Sean A. Irvine, Oct 29 2020

A036389 Number of (odd and even) split numbers (A036382) below 2^n.

Original entry on oeis.org

0, 0, 1, 4, 12, 30, 69, 150, 317, 659, 1361, 2784, 5686, 11557, 23445, 47472, 95991, 193891, 391266, 788979, 1589856, 3201863, 6445059, 12967425, 26080302, 52434693, 105386552, 211751544, 425359720, 854245385, 1715204991
Offset: 1

Views

Author

Labos Elemer

Keywords

Comments

Equivalently, number of split numbers (A036382) with binary order (A029837) <= n.
Partial sums of A036385. - Sean A. Irvine, Oct 29 2020

Examples

			The 12 odd and even split numbers below 32 are as follows: 6, 10, 12, 14, 18, 20, 21, 22, 24, 26, 28, 30.

Crossrefs

Cf. A029837 (ceiling(log_2(n))), A036382.

Extensions

Definition rephrased by M. F. Hasler, Apr 24 2017
a(21)-a(31) from Sean A. Irvine, Oct 29 2020
Showing 1-5 of 5 results.

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

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