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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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A113314 a(n) is the index k such that A111118(k) = n.

Original entry on oeis.org

1, 4, 11, 680, 2, 28, 9, 65, 7, 26, 3, 146, 5, 63, 24, 317, 22, 61, 20, 144, 3038, 18, 6, 59, 16, 8, 142, 10, 14, 57, 12, 315, 55, 140, 53, 6353, 313, 51, 138, 49, 678, 136, 47, 1441, 45, 134, 43, 311, 676, 41, 132, 13, 39, 309, 15, 37, 17, 130, 19, 35, 3036, 21, 33, 23
Offset: 1

Views

Author

Klaus Brockhaus, Oct 25 2005

Keywords

Examples

			A111118(680) = 4, hence a(4) = 680.

Crossrefs

Cf. A111118, A111187.

A111698 a(1)=1. Skipping over integers occurring earlier in the sequence, count down a composite from a(n) to get a(n+1) so that a(n+1) is the smallest possible positive integer arrived at this way. If there are no positive integers at a distance of a composite number of yet unused integers, instead count up from a(n) 4 (the lowest composite positive integer) positions (skipping already occurring integers) to get a(n+1).

Original entry on oeis.org

1, 5, 9, 2, 7, 12, 3, 10, 15, 4, 13, 18, 6, 16, 21, 8, 19, 24, 11, 22, 27, 14, 25, 30, 17, 28, 33, 20, 31, 36, 23, 34, 39, 26, 37, 42, 29, 40, 45, 32, 43, 48, 35, 46, 51, 38, 49, 54, 41, 52, 57, 44, 55, 60, 47, 58, 63, 50, 61, 66, 53, 64, 69, 56, 67, 72, 59, 70, 75, 62, 73, 78
Offset: 1

Views

Author

Leroy Quet, Nov 17 2005

Keywords

Comments

I have found two patterns for this sequence. The first is that there is a pattern 0,3,6,0,3,6,0,3,6,... which states the lengths of the "LessThanList" for each term. In other words, a(6) = 12. There are six integers less than 12 which are not already listed in the sequence at this point, {3,4,6,8,10,11}. a(7) = 3. There are no integers not already on the list which are less than 3 at this point. a(8) = 10. There are three integers less than 10 which are not already on the list at this point, {4,6,8}. Also, after the 14th term, the sequence becomes regular in the following way. The difference between successive terms is as follows: 5,-13,11,5,-13,11,... . - Diana L. Mecum, Aug 15 2008

Examples

			The first 5 terms of the sequence can be plotted on the number line as:
1,2,*,*,5,*,7,*,9,*,*,*.
Now a(5) is 7. Counting down from 7 gets a noncomposite (1,2, or 3) number of steps to arrive at each yet unused positive integer. So we instead count up 4 positions, skipping the 9 as we count, to arrive at 12 (which is at the rightmost * of the number line above).

Links

Crossrefs

Cf. A111453, A111118.

Extensions

Terms a(14) through a(1011) from Diana L. Mecum, Aug 15 2008
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