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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.

Showing 1-3 of 3 results.

A334219 a(n) is the number of terms beyond the starting value n before a repeated number first appears when following the same rules as Recamán's sequence A005132 but starting at n instead of 0.

Original entry on oeis.org

24, 13, 21, 3, 3, 3, 15, 6, 6, 6, 15, 12, 9, 9, 9, 16, 20, 15, 12, 12, 12, 8, 10, 12, 20, 15, 15, 15, 10, 15, 24, 22, 26, 18, 18, 18, 11, 13, 18, 29, 28, 27, 21, 21, 21, 15, 13, 19, 17, 25, 31, 23, 24, 24, 24, 16, 18, 20, 21, 44, 28, 34, 34, 27, 27, 27, 17, 19, 27, 25, 24
Offset: 0

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Author

Scott R. Shannon, Apr 19 2020

Keywords

Comments

The first repeated number in each sequence starting from n is given in A334148.
The number of terms in each sequence starting from n required to reach a value greater than n given in A334149.
Essentially the same as A308419. - R. J. Mathar, May 06 2020

Examples

			a(0) = 24 as a(0) corresponds to the standard Recamán's sequence A005132 in which the term 42 appears at A005132(20) and then again at A005132(24), taking twenty-four terms before the first repeated number appears.
a(4) = 3 as starting from 4 the sequence of visited numbers is 4,3,1,4 and it takes three steps beyond the start value for the first repeated number 4 to appear.
a(6) = 15 as starting from 6 the sequence of visited numbers is 6,5,3,0,4,9,15,8,16,7,17,28,40,27,13,28 and it takes fifteen steps beyond the start value for the first repeated number 28 to appear.

Links

Crossrefs

Cf. A005132, A308419, A334148, A334149, A334225.

A334148 a(n) is the first term to repeat when following the same rules as Recamán's sequence A005132 but starting at n instead of 0.

Original entry on oeis.org

42, 20, 33, 3, 4, 5, 28, 6, 7, 8, 16, 15, 9, 10, 11, 19, 24, 21, 12, 13, 14, 15, 19, 23, 26, 15, 16, 17, 27, 21, 42, 44, 49, 18, 19, 20, 30, 36, 27, 48, 34, 59, 21, 22, 23, 21, 25, 29, 33, 36, 40, 45, 24, 25, 26, 23, 27, 31, 55, 79, 42, 46, 49, 27, 28, 29, 25, 29
Offset: 0

Views

Author

Scott R. Shannon, Apr 16 2020

Keywords

Comments

The terms of this sequence grow slowly as n increases and are confined to bands of certain values, see the link image. Between n = 998000 and n = 1000000 the smallest term is 2829 and the largest is 19331.
The number of terms in each sequence starting from n required to reach a(n) is given in A334219.
The values where a(n) = n are given in A334225.
The number of terms in each sequence starting from n required to reach a value greater than n given in A334149.

Examples

			a(0) = 42 as a(0) corresponds to the standard Recamán's sequence A005132 in which 42 is the first term to repeat, appearing at A005132(20) and then again at A005132(24).
a(3) = 3 as starting from 3 the sequence of visited numbers is 3,2,0,3 and 3 is the first term to repeat.
a(6) = 28 as starting from 6 the sequence of visited numbers is 6,5,3,0,4,9,15,8,16,7,17,28,40,27,13,28 and 28 is the first number to repeat.

Links

Crossrefs

Cf. A005132, A334149, A334219, A334225.

A334149 a(n) is the number of terms required beyond the starting value n before a value larger than n first appears when following the same rules as Recamán's sequence A005132 but starting at n instead of 0.

Original entry on oeis.org

1, 2, 2, 4, 5, 5, 5, 7, 9, 10, 6, 8, 10, 12, 14, 8, 9, 11, 13, 15, 17, 9, 11, 13, 14, 16, 18, 20, 20, 12, 14, 16, 17, 19, 21, 23, 23, 14, 15, 17, 19, 21, 22, 24, 26, 26, 30, 34, 18, 20, 22, 24, 26, 28, 29, 29, 33, 37, 37, 21, 23, 25, 27, 29, 31, 33, 33, 36, 19, 40, 44, 27, 26, 28
Offset: 0

Views

Author

Scott R. Shannon, Apr 16 2020

Keywords

Comments

For 100 <= n <= 100000 the largest number of terms to surpass the starting value n is for n = 97646 which takes 26867 terms to surpass 97646, see the link image. The longest in terms of ratio of terms required compared to starting value is for n = 133 which takes 80 terms, see the link image. The shortest ratio is for n = 82148 which only takes 8587, see the link image.
The first repeated number in each sequence starting from n is given in A334148.
The number of terms in each sequence starting from n required to reach the first repeated number is given in A334219.

Examples

			a(0) = 1 as a(0) corresponds to the standard Recamán's sequence A005132 in which the first term is 0 and it only takes one more term to reach 1 and surpass the start value.
a(4) = 5 as starting from 4 the sequence of visited numbers is 4,3,1,4,0,5 and it takes five more terms to reach 5 and surpass the start value 4.
a(12) = 10 as starting from 12 the sequence of visited numbers is 12,11,9,6,2,7,1,8,0,9,19 and it takes ten more terms to reach 19 and surpass the start value 12.

Links

Crossrefs

Cf. A005132, A334148, A334219, A334225.
Showing 1-3 of 3 results.

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