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.

A371904 a(1) = 1; for n > 1, a(n) is the smallest unused positive number such that 2^a(n) contains a(n-1) as a substring.

Original entry on oeis.org

1, 4, 2, 5, 8, 3, 14, 18, 30, 22, 43, 25, 41, 44, 38, 23, 58, 33, 63, 55, 16, 24, 10, 17, 27, 15, 21, 31, 49, 32, 45, 28, 7, 20, 11, 40, 12, 9, 13, 37, 47, 36, 29, 60, 59, 35, 52, 19, 53, 79, 34, 65, 42, 50, 54, 39, 61, 62, 66, 46, 64, 6, 26, 71, 48, 51, 57, 56, 68, 75, 67, 78, 74, 70, 69, 72
Offset: 1

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Author

Scott R. Shannon, Apr 11 2024

Keywords

Comments

The sequence is conjectured to be a permutation of the positive integers.

Examples

			a(2) = 4 as 2^4 = 16 which contains a(n-1) = a(1) = '1' as a substring.
a(7) = 14 as 2^14 = 16384 which contains a(n-1) = a(6) = '3' as a substring. Note that 2^5 = 32 also contains '3' as a substring but 5 has already been used.
		

Crossrefs

A371918 The smallest unused positive number such that 2^a(n) contains n as a substring.

Original entry on oeis.org

10, 4, 1, 5, 2, 8, 6, 15, 3, 12, 17, 40, 7, 27, 18, 21, 14, 34, 30, 13, 11, 24, 43, 41, 19, 50, 28, 38, 47, 32, 22, 49, 25, 63, 33, 35, 16, 37, 23, 42, 53, 44, 59, 45, 46, 52, 60, 31, 20, 39, 54, 9, 51, 29, 74, 57, 48, 56, 61, 69, 55, 58, 66, 76, 26, 73, 72, 36, 62, 82, 64, 70, 77, 67, 65, 91, 78
Offset: 0

Views

Author

Scott R. Shannon, Apr 12 2024

Keywords

Comments

The sequence is conjectured to be a permutation of the positive integers.

Examples

			a(0) = 10 as 2^10 = 1024 which contains '0' as a substring.
a(6) = 6 as 2^6 = 64 which contains '6' as a substring. Note that 2^4 also contains '6' but 4 has already been used. This is the first term to differ from A063565.
		

Crossrefs

A375958 The smallest positive number that when written in all bases 2 to n contains two or more adjacent equal digits.

Original entry on oeis.org

3, 4, 22, 31, 43, 122, 506, 506, 1187, 3199, 11663, 18773, 18815, 32399, 177216, 177216, 177227, 5225284, 5225284, 14295600, 21566225, 36572552, 107730081, 107832239, 952416000, 2293096006, 5587865542, 6587515515, 30174888567, 30174888567, 107824082399
Offset: 2

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Author

Scott R. Shannon, Sep 03 2024

Keywords

Examples

			a(7) = 122 as 122 = 1111010_2 = 11112_3 = 1322_4 = 442_5 = 322_6 = 233_7, each of which contains two or more adjacent equal digits.
		

Crossrefs

A375997 The smallest positive number that when written in all bases 2 to n contains three or more adjacent equal digits.

Original entry on oeis.org

7, 39, 234, 687, 3882, 13999, 196017, 786499, 2790000, 3898880, 150002496, 150002496, 22094555327, 164777407488
Offset: 2

Views

Author

Scott R. Shannon, Sep 05 2024

Keywords

Examples

			a(7) = 13999 as 13999 = 11011010101111_2 = 201012111_3 = 3122233_4 = 421444_5 = 144451_6 = 55546_7, each of which contains three or more adjacent equal digits.
		

Crossrefs

A375998 The smallest positive number that when written in all bases 2 to n contains four or more adjacent equal digits.

Original entry on oeis.org

15, 80, 4010, 12031, 255312, 2686719, 117178358, 436210878, 91532745555
Offset: 2

Views

Author

Scott R. Shannon, Sep 05 2024

Keywords

Examples

			a(7) = 2686719 as 2686719 = 1010001111111011111111_2 = 12001111111010_3 = 22033323333_4 = 1141433334_5 = 133330303_6 = 31560000_7, each of which contains four or more adjacent equal digits.
		

Crossrefs

Showing 1-5 of 5 results.