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.

A354679 First differences of A354575.

Original entry on oeis.org

1, 3, -2, 4, -3, 5, -1, 7, -4, -5, 11, -7, 9, -6, 8, 2, -11, 13, -9, 15, -17, 19, -13, 17, -19, 23, -15, 21, -25, 27, -22, 16, -14, 6, 18, -29, 31, -27, 29, -23, 25, -21, 33, -41, 37, -35, 41, -37, 43, -40, 22, -16, 32, -31, 35, 10, -51, 47, -43, 39, -33, 49, -47, 45, -55, 53, -44, 14, 24, -26
Offset: 1

Views

Author

Scott R. Shannon, Jun 05 2022

Keywords

Comments

See A354575 for further details.

Examples

			a(3) = -2 as A354575(4) - A354575(3) = 3 - 5 = -2.

Links

Crossrefs

Cf. A354575, A354688, A354727, A354739, A354687.

A354727 a(1) = 1; for n > 1, a(n) is the smallest positive number that has not yet appeared that shares a factor with a(n-1) and the difference a(n) - a(n-1) is distinct from all previous differences.

Original entry on oeis.org

1, 2, 4, 8, 6, 3, 9, 12, 20, 5, 10, 22, 11, 33, 15, 24, 14, 7, 21, 28, 16, 26, 13, 39, 18, 34, 17, 51, 27, 42, 36, 32, 50, 25, 45, 40, 64, 30, 55, 35, 56, 48, 75, 66, 38, 19, 57, 76, 44, 72, 46, 23, 69, 92, 52, 65, 95, 60, 93, 31, 62, 94, 47, 141, 54, 90, 63, 49, 84, 68, 85, 125, 70, 112, 58
Offset: 1

Views

Author

Scott R. Shannon, Jun 05 2022

Keywords

Comments

This sequences uses similar a similar rule to A354687 but here the sign of the difference between a(n-1) and a(n) is considered. The terms show an overall similar behavior to A354687 although here only two lines show a higher concentration of terms than the other lines. See the linked image.
In the first 100000 terms the fixed points are 1,2,15,32,100,115,300,720. It is plausible no more exist although this is unknown.. The sequence is conjectured to be a permutation of the positive integers.
See A354739 for the differences between terms.

Examples

			a(9) = 20 as a(8) = 12, and 20 is the smallest unused number that shares a factor with 12 and whose difference from the previous term, 20 - 12 = 8, has not appeared. Note that 10,14,15,16,18 all share a factor with 12 but their differences from 12, namely -2,2,3,4,6, have already appeared as differences between previous pairs of terms.

Links

Crossrefs

Cf. A354739, A354687, A354575, A354679, A354688.

A354739 First differences of A354727.

Original entry on oeis.org

1, 2, 4, -2, -3, 6, 3, 8, -15, 5, 12, -11, 22, -18, 9, -10, -7, 14, 7, -12, 10, -13, 26, -21, 16, -17, 34, -24, 15, -6, -4, 18, -25, 20, -5, 24, -34, 25, -20, 21, -8, 27, -9, -28, -19, 38, 19, -32, 28, -26, -23, 46, 23, -40, 13, 30, -35, 33, -62, 31, 32, -47, 94, -87, 36, -27, -14, 35, -16, 17
Offset: 1

Views

Author

Scott R. Shannon, Jun 05 2022

Keywords

Comments

See A354727 for further details.

Examples

			a(5) = -3 as A354727(6) - A354727(5) = 3 - 6 = -3.

Links

Crossrefs

Cf. A354727, A354687, A354575, A354679, A354688.
Showing 1-3 of 3 results.

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

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