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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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A281409 Lexicographically first sequence of distinct terms, beginning with a(1)=5, with the property that each triple of consecutive terms contains a term that divides the sum of the other two terms.

Original entry on oeis.org

5, 1, 2, 3, 4, 7, 9, 8, 10, 6, 14, 16, 12, 20, 28, 24, 13, 11, 15, 18, 21, 33, 27, 30, 19, 41, 22, 25, 47, 36, 58, 50, 42, 23, 61, 31, 32, 63, 65, 64, 43, 85, 44, 91, 45, 17, 40, 57, 74, 97, 51, 37, 60, 83, 106, 129, 152, 175, 109, 66, 35, 39, 82, 113, 133, 93
Offset: 1

Views

Author

Rémy Sigrist, Jan 21 2017

Keywords

Comments

The initial term a(1)=5 seems to be the least one that leads to a sequence that is not ultimately linear.
The variant with:
- a(1)=1 matches A000027,
- a(1)=2 matches A181440,
- a(1)=3 starts with 3, 1, 2, and then matches A000027,
- a(1)=4 starts with 4, 1, 2, and then matches A143097,
- a(1)=6 starts with 6, 1, 2, 3, 4, 5, and then matches A000027,
- a(1)=9 starts with 9, 1, 2, 3, 4, 5, 6, 7, 8, 13, 11, 12, 10, and then matches A143097.
Conjecturally, all other variants are not ultimately linear.

Examples

			The first terms, alongside the indexes of the terms that divide the sum of the other two terms within the n-th triple of consecutive terms, are:
   n  a(n)   Indexes
  --  ----   -------
   1    5    2, 3
   2    1    1, 2, 3
   3    2    2
   4    3    3
   5    4    1
   6    7    3
   7    9    1
   8    8    1, 3
   9   10    1, 2
  10    6    1
  11   14    1
  12   16    1, 2
  13   12    1, 2
  14   20    3
  15   28    3
  16   24    1
  17   13    1
  18   11    1
  19   15    2
  20   18    1
  21   21    3
  22   33    3
  23   27    3
  24   30    1
  25   19    2

Links

Crossrefs

Cf. A000027, A143097, A181440, A278962, A281408.

A171950 a(1)=1. a(n) = the absolute difference between (the sum of previous terms) and A000217(n-2), n>1.

Original entry on oeis.org

1, 1, 1, 0, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21, 22, 23, 24, 25, 26, 27, 28, 29, 30, 31, 32, 33, 34, 35, 36, 37, 38, 39, 40, 41, 42, 43, 44, 45, 46, 47, 48, 49, 50, 51, 52, 53, 54, 55, 56, 57, 58, 59, 60, 61, 62, 63, 64, 65, 66, 67, 68
Offset: 1

Views

Author

Giovanni Teofilatto, Oct 20 2010

Keywords

Links

Crossrefs

Cf. A000217, A065475.

Programs

Formula

a(n) = |Sum_{i=1..n-1} a(i) - A000217(n-2)|, n>1.
a(n) = n-2, n>=5. - R. J. Mathar, Oct 26 2010

Extensions

Zero inserted, precise indices added in definition, keyword:less and two formulas added - R. J. Mathar, Oct 26 2010
A171950 and A181440 are two different edited versions of a sequence submitted by Giovanni Teofilatto. - N. J. A. Sloane, Oct 29 2010
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