A340593 a(0) = 0; for n > 0, if n appears in the sequence then a(n) = a(n-1) - lastindex(n) if nonnegative and not already in the sequence, otherwise a(n) = a(n-1) + lastindex(n), where lastindex(n) is the index of the last appearance of n. Otherwise a(n) = a(n-1) - n if nonnegative and not already in the sequence, otherwise a(n) = a(n-1) + n.

0, 1, 3, 5, 9, 6, 11, 4, 12, 8, 18, 24, 16, 29, 15, 29, 17, 33, 23, 42, 22, 43, 63, 45, 34, 59, 85, 58, 30, 45, 73, 104, 72, 55, 31, 66, 102, 65, 27, 66, 26, 67, 48, 69, 25, 54, 100, 53, 95, 46, 96, 147, 199, 152, 107, 74, 130, 187, 160, 135, 75, 14, 76, 98, 162, 125, 86, 127, 195, 238, 168, 97

Offset: 0

Author

Scott R. Shannon, Jan 13 2021

Keywords

• nonn

Comments

This sequences uses the same rules as Recamán's sequence A005132 if the value of n itself has not previously appeared in the sequence. However if n has previously appeared then the step size from a(n-1) is set to lastindex(n), where lastindex(n) is the sequence index of the last appearance of n.

The smallest value not to have appeared after 1 million terms is 52. It is unknown if all terms eventually appear.

Examples

			a(3) = 5 as a(2) = 3 = n, thus the step size from a(2) is 2. As 1 has previously appeared a(3) = a(2) + 2 = 3 + 2 = 5.
a(5) = 6 as a(3) = 5 = n, thus the step size from a(4) is 3. As 6 has not previously appeared a(5) = a(4) - 3 = 9 - 3 = 6.
		

Crossrefs

Cf. A005132, A339673, A340612, A336760, A336761.

Programs

Python

from itertools import count, islice
def A340593_gen(): # generator of terms
    a, ndict = 0, {0:0}
    yield 0
    for n in count(1):
        yield (a:= (a-m if a>=(m:=ndict[n]) and a-m not in ndict else a+m) if n in ndict else (a-n if a>=n and a-n not in ndict else a+n))
        ndict[a] = n
A340593_list = list(islice(A340593_gen(),30)) # Chai Wah Wu, Jun 29 2023