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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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.

A334225 The values n where A334148(n) = n.

Original entry on oeis.org

3, 4, 5, 23, 140, 290
Offset: 0

Views

Author

Scott R. Shannon, Apr 19 2020

Keywords

Comments

See A334148 for the definition of the sequence and a plot of other n values.
There are no other values for n up to 1000000. As A334148(n) increase slowly for n, for example A334148(1000000) = 6655, it is almost certain that no other values exist.

Examples

			3 is a term as starting from 3 the sequence of visited numbers is 3,2,0,3 and 3 is the first term to repeat.
23 is a term as starting from 23 the sequence of visited numbers is 23,22,20,17,13,8,2,9,1,10,0,11,23 and 23 is the first term to repeat.
290 is a term as starting from 290 the sequence of visited numbers is 290,289,287,284,280,275,269,262,254,245,235,224,212,199,185,170,154,137,119,100,80,59,37,14,38,13,39,12,40,11,41,10,42,9,43,8,44,7,45,6,46,5,47,4,48,3,49,2,50,1,51,0,52,105,159,104,160,103,161,102,162,101,163,226,290 and 290 is the first term to repeat. This is almost certainly the largest such value.

Links

Crossrefs

Cf. A005132, A334148, A334149, A334219.
Showing 1-3 of 3 results.

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

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