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.

A126917 a(1)=1. a(n) = the (largest proper divisor of n)th integer from among those positive integers not occurring earlier in the sequence.

Original entry on oeis.org

1, 2, 3, 5, 4, 8, 6, 11, 10, 14, 7, 17, 9, 20, 18, 23, 12, 26, 13, 29, 25, 32, 15, 35, 24, 38, 33, 41, 16, 44, 19, 47, 40, 50, 34, 53, 21, 56, 48, 59, 22, 62, 27, 65, 55, 68, 28, 71, 43, 74, 63, 77, 30, 80, 54, 83, 70, 86, 31, 89, 36, 92, 78, 95, 64, 98, 37, 101, 85, 104, 39
Offset: 1

Views

Author

Leroy Quet, Dec 31 2006

Keywords

Comments

Sequence is a permutation of the positive integers.

Examples

			The largest proper divisor of 8 is 4. So a(8) is the 4th integer from among those not occurring among the first 7 integers of the sequence (a(8) is the 4th integer from among 7,9,10,11,13,14,..). So a(8) = 11.

Links

Crossrefs

Cf. A126918, A032742, A243069, A243488.

Programs

  • Mathematica
    f[l_List] := Block[{k = 0, c = Divisors[Length[l] + 1][[ -2]]},While[c > 0,k++;While[MemberQ[l, k], k++ ];c--;];Append[l, k]];Nest[f, {1}, 71] (* Ray Chandler, Jan 04 2007 *)

Extensions

Extended by Ray Chandler, Jan 04 2007

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

Views

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.

Links

Crossrefs

Cf. A126917, A126918, A243488, A243498.

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).

A243498 Records (and distinct values) of A243069: a(n) = A243069(A008578(n)).

Original entry on oeis.org

2, 3, 4, 6, 7, 9, 12, 13, 15, 16, 19, 21, 22, 27, 28, 30, 31, 36, 37, 39, 42, 45, 46, 49, 51, 52, 57, 58, 60, 61, 66, 69, 72, 73, 75, 76, 81, 82, 87, 88, 91, 96, 97, 99, 102, 105, 109, 111, 112, 118, 120, 126, 127, 129, 132, 133, 135, 136, 142, 147, 148, 150
Offset: 1

Views

Author

Antti Karttunen, Jun 21 2014

Keywords

Links

Crossrefs

Cf. A243069, A243488, A126917, A008578.

Programs

Formula

a(n) = A243069(A008578(n)).
Showing 1-3 of 3 results.

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

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