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.

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

Author

Scott R. Shannon, Apr 16 2020

Keywords

• nonn

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

• 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

Crossrefs

Cf. A005132, A334148, A334219, A334225.