A334148 -id:A334148 - cp's OEIS frontend

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

3, 4, 5, 23, 140, 290

Offset: 0

Scott R. Shannon, Apr 19 2020

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.

			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.

Index entries for sequences related to Recamán's sequence

Cf. A005132, A334148, A334149, A334219.

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

Scott R. Shannon, Apr 19 2020

nonn

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

			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.

Scott R. Shannon, Table of n, a(n) for n = 0..10000
Scott R. Shannon, Plot of the terms for n = 0 to 1000000
Index entries for sequences related to Recamán's sequence

Cf. A005132, A308419, A334148, A334149, 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

Scott R. Shannon, Apr 16 2020

nonn

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.

			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.

Scott R. Shannon, Table of n, a(n) for n = 0..10000
Scott R. Shannon, Line plot of the corresponding Recamán type sequence starting with n = 97646.
Scott R. Shannon, Line plot of the corresponding Recamán type sequence starting with n = 133.
Scott R. Shannon, Line plot of the corresponding Recamán type sequence starting with n = 82148.
Scott R. Shannon, Plot of this sequence's terms for n = 0 to 100000.
Index entries for sequences related to Recamán's sequence

Cf. A005132, A334148, A334219, A334225.

cp's OEIS Frontend

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

Views

Author

Keywords

Comments

Examples

Links

Crossrefs

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.

Views

Author

Keywords

Comments

Examples

Links

Crossrefs

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.

Views

Author

Keywords

Comments

Examples

Links

Crossrefs