OFFSET
0,2
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.
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.
EXAMPLE
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.
CROSSREFS
KEYWORD
nonn
AUTHOR
Scott R. Shannon, Apr 16 2020
STATUS
approved