A362373 a(0) = 0; for n > 0, if n appears in the sequence then a(n) is the sum of the indices of all previous appearances 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, 2, 6, 11, 4, 11, 19, 10, 9, 12, 11, 24, 38, 23, 7, 24, 42, 8, 28, 49, 27, 15, 30, 5, 31, 22, 20, 49, 24, 26, 58, 25, 59, 94, 130, 93, 14, 53, 13, 54, 18, 61, 17, 62, 16, 63, 111, 50, 49, 100, 48, 39, 41, 96, 40, 97, 32, 34, 94

Offset: 0

Author

Kelvin Voskuijl, Apr 17 2023

Keywords

• nonn
• look
• easy

Comments

Conjecture: All nonnegative integers appear in this sequence. - Yifan Xie, Apr 24 2023

Examples

			a(2) = 3 = n, thus a(3) = 2.
a(5) = 11, as 5 has not previously appeared in the sequence, but a(4) - 5 = 1 has, thus a(5) = a(4) + 5 = 6 + 5 = 11.
a(5) and a(7) = 11, and 5 + 7 = 12, thus a(11) = 12.
		

Links

• Michael De Vlieger, Table of n, a(n) for n = 0..16384
• Michael De Vlieger, Log log scatterplot of a(n), n = 1..2^14.
• Michael De Vlieger, Log log scatterplot of a(n), n = 1..2^20

Crossrefs

Cf. A005132, A340612.

Programs

Mathematica

nn = 120; c[] := 0; j = a[0] = 0; Do[If[# > 0, Set[k, #], If[And[n <= j, c[#] == 0], Set[k, #], Set[k, j + n]] &[j - n] ] &[c[n]]; c[k] += n; Set[{a[n], j}, {k, k}], {n, nn}]; Array[a, nn, 0] (* _Michael De Vlieger, Apr 19 2023 *)

Python

from itertools import count, islice
def A362373_gen(): # generator of terms
    a, ndict = 0, {0:0}
    yield 0
    for n in count(1):
        yield (a:= ndict[n] if n in ndict else (a-n if a>=n and a-n not in ndict else a+n))
        ndict[a] = ndict.get(a,0)+n
A363373_list = list(islice(A362373_gen(),30)) # Chai Wah Wu, Jun 29 2023