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.

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

Author

Scott R. Shannon, Apr 16 2020

Keywords

• nonn

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

• 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

Crossrefs

Cf. A005132, A334149, A334219, A334225.