

A323420


Lexicographically earliest sequence of positive integers such that for any n > 0, a(n + a(n)) > a(n).


1



1, 2, 1, 3, 1, 2, 4, 3, 1, 2, 5, 3, 1, 2, 4, 6, 1, 2, 5, 3, 1, 7, 4, 6, 1, 2, 5, 3, 8, 7, 4, 6, 1, 2, 5, 3, 9, 7, 4, 6, 1, 2, 5, 3, 8, 10, 4, 6, 1, 2, 5, 3, 9, 7, 4, 11, 1, 2, 5, 3, 8, 10, 4, 6, 1, 2, 12, 3, 9, 7, 4, 11, 1, 2, 5, 3, 8, 10, 13, 6, 1, 2, 12, 3
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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 runlength transform of the first differences of the positions of the 1's in the sequence corresponds to A055010 (excluding the leading 0).


LINKS



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



STATUS

approved



