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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.
4
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
0,1
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.
EXAMPLE
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.
CROSSREFS
KEYWORD
nonn
AUTHOR
Scott R. Shannon, Apr 16 2020
STATUS
approved