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A360265
a(0) = 0, and for any n > 0, let k > 0 be as small as possible and such that t(k) >= n (where t(m) denotes A000217(m), the m-th triangular number); a(n) = k + a(t(k) - n).
2
0, 1, 3, 2, 6, 4, 3, 6, 7, 5, 4, 11, 7, 8, 6, 5, 10, 12, 8, 9, 7, 6, 10, 11, 13, 9, 10, 8, 7, 14, 11, 12, 14, 10, 11, 9, 8, 16, 15, 12, 13, 15, 11, 12, 10, 9, 15, 17, 16, 13, 14, 16, 12, 13, 11, 10, 15, 16, 18, 17, 14, 15, 17, 13, 14, 12, 11, 23, 16, 17, 19
OFFSET
0,3
COMMENTS
See A002024 for the corresponding k's.
See A360259 for similar sequences.
LINKS
FORMULA
a(A000217(n)) = n.
EXAMPLE
The first terms, alongside the corresponding k's, are:
n a(n) k
-- ---- ---
0 0 N/A
1 1 1
2 3 2
3 2 2
4 6 3
5 4 3
6 3 3
7 6 4
8 7 4
9 5 4
10 4 4
11 11 5
12 7 5
PROG
(PARI) { print1 (0); t = 0; k = 0; for (n = 1, #a = vector(70), if (t < n, t += k++; ); print1 (", "a[n] = k + if (t==n, 0, a[t-n])); ); }
CROSSREFS
KEYWORD
nonn,look
AUTHOR
Rémy Sigrist, Jan 31 2023
STATUS
approved