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.

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A243069 a(n) = smallest natural number that has not yet occurred among the first n terms of A126917.

Original entry on oeis.org

2, 3, 4, 4, 6, 6, 7, 7, 7, 7, 9, 9, 12, 12, 12, 12, 13, 13, 15, 15, 15, 15, 16, 16, 16, 16, 16, 16, 19, 19, 21, 21, 21, 21, 21, 21, 22, 22, 22, 22, 27, 27, 28, 28, 28, 28, 30, 30, 30, 30, 30, 30, 31, 31, 31, 31, 31, 31, 36, 36, 37, 37, 37, 37, 37, 37, 39, 39, 39, 39, 42, 42, 45
Offset: 1

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Author

Antti Karttunen, Jun 20 2014

Keywords

Comments

Facilitates the computing of A126917.
a(n) grows only when n is a prime. A243498 gives the values at those points.

Examples

			The first eight terms of A126917 are: 1, 2, 3, 5, 4, 8, 6, 11. In range [1,1] the first that has not yet occurred is 2, in range [1,2] it is 3, in range [1,3] it is 4, in range [1,4] it is still 4, in range [1,5] it is 6, in range [1,6] it is still 6, in range [1,7] it is 7, in range [1,8] it is still 7, thus the first eight terms of this sequence are 2, 3, 4, 4, 6, 6, 7, 7.
		

Crossrefs

Formula

For all n, a(n) <= A126917(n+1).
For n >= 2, if A126917(n) > a(n-1) [when n is composite], a(n) = a(n-1).

A243488 a(n) = A126917(n+1) - A243069(n).

Original entry on oeis.org

0, 0, 1, 0, 2, 0, 4, 3, 7, 0, 8, 0, 8, 6, 11, 0, 13, 0, 14, 10, 17, 0, 19, 8, 22, 17, 25, 0, 25, 0, 26, 19, 29, 13, 32, 0, 34, 26, 37, 0, 35, 0, 37, 27, 40, 0, 41, 13, 44, 33, 47, 0, 49, 23, 52, 39, 55, 0, 53, 0, 55, 41, 58, 27, 61, 0, 62, 46, 65, 0, 65, 0, 65, 48, 68, 22, 71, 0
Offset: 1

Views

Author

Antti Karttunen, Jun 20 2014

Keywords

Comments

Zeros occur at positions given by A006093 (primes minus 1).
The sequence sheds some light on behavior of A126917, please see the plot.

Crossrefs

Programs

Formula

a(n) = A126917(n+1) - A243069(n).
Showing 1-2 of 2 results.