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%I #9 Feb 02 2023 14:43:17
%S 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,
%T 11,12,14,10,11,9,8,16,15,12,13,15,11,12,10,9,15,17,16,13,14,16,12,13,
%U 11,10,15,16,18,17,14,15,17,13,14,12,11,23,16,17,19
%N 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).
%C See A002024 for the corresponding k's.
%C See A360259 for similar sequences.
%H Rémy Sigrist, <a href="/A360265/b360265.txt">Table of n, a(n) for n = 0..10000</a>
%F a(A000217(n)) = n.
%e The first terms, alongside the corresponding k's, are:
%e n a(n) k
%e -- ---- ---
%e 0 0 N/A
%e 1 1 1
%e 2 3 2
%e 3 2 2
%e 4 6 3
%e 5 4 3
%e 6 3 3
%e 7 6 4
%e 8 7 4
%e 9 5 4
%e 10 4 4
%e 11 11 5
%e 12 7 5
%o (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]));); }
%Y Cf. A000217, A002024, A360259.
%K nonn,look
%O 0,3
%A _Rémy Sigrist_, Jan 31 2023
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