OFFSET
1,2
COMMENTS
Every positive integer appears in the sequence.
Empirically:
- for any n > 0, the least d > 0 such that a(n) = a(n+d) is a power of 2 (see scatterplot in Links section),
- the run-length transform of the first differences of the positions of the 1's in the sequence corresponds to A055010 (excluding the leading 0).
LINKS
Rémy Sigrist, Table of n, a(n) for n = 1..10000
Rémy Sigrist, Colored scatterplot of the first 100000 terms (where the color is function of the least d > 0 such that a(n) = a(n+d))
FORMULA
a(A000124(n)) = n + 1 for any n >= 0.
EXAMPLE
a(1) = 1, hence a(1 + a(1)) = a(2) > 1.
a(2) = 2, hence a(2 + a(2)) = a(4) > 2.
a(3) = 1, hence a(3 + a(1)) = a(4) > 1.
a(4) = 3, etc.
PROG
(PARI) a = vector(84, n, 1); for (n=1, #a, print1 (a[n] ", "); nan = n+a[n]; if (nan <= #a, a[nan] = max(a[nan], 1+a[n])))
CROSSREFS
KEYWORD
nonn
AUTHOR
Rémy Sigrist, Aug 30 2019
STATUS
approved