A100037 Positions of occurrences of the natural numbers as a second subsequence in A100035.

4, 9, 18, 31, 48, 69, 94, 123, 156, 193, 234, 279, 328, 381, 438, 499, 564, 633, 706, 783, 864, 949, 1038, 1131, 1228, 1329, 1434, 1543, 1656, 1773, 1894, 2019, 2148, 2281, 2418, 2559, 2704, 2853, 3006, 3163, 3324, 3489, 3658, 3831, 4008, 4189, 4374, 4563

Offset: 1

Author

Reinhard Zumkeller, Oct 31 2004

Keywords

• nonn

Comments

For n > 1, A100035(a(n)) = n and A100035(m) != n for a(n-1) <= m < a(n);

A100036(n) < a(n) < A100038(n) < A100039(n).

Examples

			First terms (10 = A, 11 = B, 12 = C) of A100035(a(n)):
...1....2........3............4................5......
1231435425165764736271879869584938291A9BA8B7A6B5A4B3A2B;
a(1) = A084849(2) = 4, A100035(4) = 1;
a(2) = A014107(2) = 9, A100035(9) = 2;
a(3) = A033537(3) = 18, A100035(18) = 3;
a(4) = A100040(4) = 31, A100035(31) = 4;
a(5) = A100041(5) = 48, A100035(48) = 5.
		

Links

• Guo-Niu Han, Enumeration of Standard Puzzles, 2011. [Cached copy]
• Guo-Niu Han, Enumeration of Standard Puzzles, arXiv:2006.14070 [math.CO], 2020.

Crossrefs

Cf. A014107, A033537, A084849, A100035, A100036, A100038, A100039, A100040, A100041.

Formula

a(n) = 2*n^2 - n + 3 (conjectured). - Ralf Stephan, May 15 2007