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.

A321318 Number of distinct values obtained by partitioning the binary representation of n into consecutive blocks, and then summing the numbers represented by the blocks.

Original entry on oeis.org

1, 2, 2, 3, 3, 3, 3, 4, 4, 5, 5, 5, 5, 5, 5, 5, 5, 7, 7, 7, 7, 8, 8, 7, 7, 9, 9, 8, 8, 7, 7, 6, 6, 9, 9, 9, 9, 10, 10, 9, 9, 9, 9, 12, 12, 13, 13, 9, 9, 12, 12, 12, 12, 12, 12, 12, 12, 14, 14, 12, 12, 11, 11, 7, 7, 11, 11, 12, 12, 13, 13, 12, 12, 15, 15, 15
Offset: 1

Views

Author

Jeffrey Shallit, Nov 04 2018

Keywords

Examples

			For n = 13, we can partition its binary representation as follows (showing partition and sum of terms): (1101):13, (1)(101):6, (11)(01):4, (110)(1):7, (1)(1)(01):3, (1)(10)(1):4, (11)(0)(1):4, (1)(1)(0)(1):3.  Thus there are 5 distinct values.

Links

Crossrefs

Cf. A321319, A321320, A321321.

Programs

  • PARI
    See Links section

A321319 Smallest power of 2 obtainable by partitioning the binary representation of n into consecutive blocks and then summing.

Original entry on oeis.org

1, 1, 2, 1, 2, 2, 4, 1, 2, 2, 4, 2, 4, 4, 4, 1, 2, 2, 4, 2, 4, 4, 4, 2, 4, 4, 4, 4, 4, 4, 16, 1, 2, 2, 4, 2, 4, 4, 4, 2, 4, 4, 4, 4, 4, 4, 8, 2, 4, 4, 4, 4, 4, 4, 8, 4, 4, 4, 8, 4, 8, 8, 8, 1, 2, 2, 4, 2, 4, 4, 4, 2, 4, 4, 4, 4, 4, 4, 8, 2, 4, 4, 4, 4, 4, 4
Offset: 1

Views

Author

Jeffrey Shallit, Nov 04 2018

Keywords

Examples

			For n = 13, we can partition its binary representation as follows (showing partition and sum of terms): (1101):13, (1)(101):6, (11)(01):4, (110)(1):7, (1)(1)(01):3, (1)(10)(1):4, (11)(0)(1):4, (1)(1)(0)(1):3.  Thus the smallest power of 2 is 4.

Links

Crossrefs

Cf. A321318, A321320, A321321.

A321320 Largest power of 2 obtainable by partitioning the binary representation of n into consecutive blocks and then summing.

Original entry on oeis.org

1, 2, 2, 4, 2, 2, 4, 8, 2, 4, 4, 2, 4, 4, 8, 16, 2, 4, 4, 4, 4, 8, 8, 2, 4, 8, 8, 4, 8, 8, 16, 32, 2, 4, 4, 8, 4, 8, 8, 4, 4, 4, 8, 8, 8, 16, 16, 2, 4, 8, 8, 8, 8, 8, 16, 4, 8, 16, 16, 8, 16, 16, 32, 64, 2, 4, 4, 8, 4, 8, 8, 8, 4, 8, 8, 16, 8, 16, 16, 4, 4, 8
Offset: 1

Views

Author

Jeffrey Shallit, Nov 04 2018

Keywords

Examples

			For n = 13, we can partition its binary representation as follows (showing partition and sum of terms): (1101):13, (1)(101):6, (11)(01):4, (110)(1):7, (1)(1)(01):3, (1)(10)(1):4, (11)(0)(1):4, (1)(1)(0)(1):3.  Thus the largest power of 2 is 4.

Links

Crossrefs

Cf. A321318, A321319, A321321.

A306922 Number of distinct powers of two obtained by breaking the binary representation of n into consecutive blocks, and then adding the numbers represented by the blocks.

Original entry on oeis.org

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

Views

Author

Peter Kagey, Mar 16 2019

Keywords

Comments

1's appear at indices given by A321321.

Examples

			For n = 46, the a(46) = 3 powers of two that come from the partition of "101110" are 4, 8, and 16:
[10, 1110]         -> [2, 14]            -> 16
[1, 0, 1, 110]     -> [1, 0, 1, 6]       -> 8
[101, 1, 10]       -> [5, 1, 2]          -> 8
[1, 0, 111, 0]     -> [1, 0, 7, 0]       -> 8
[101, 11, 0]       -> [5, 3, 0]          -> 8
[1, 0, 1, 1, 1, 0] -> [1, 0, 1, 1, 1, 0] -> 4

Links

Crossrefs

Cf. A306921, A321318, A321319, A321320, A321321.
Showing 1-4 of 4 results.

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