A293866 For n > 2: when computing A229037(n), there are up to floor((n-1)/2) forbidden values (i.e. values that would lead to an arithmetic progression); a(n) = greatest forbidden value when computing A229037(n).

1, 3, 3, 1, 3, 3, 6, 6, 7, 7, 7, 7, 7, 7, 7, 6, 6, 7, 7, 7, 7, 7, 11, 11, 12, 13, 14, 12, 13, 14, 14, 15, 16, 14, 15, 16, 16, 17, 17, 16, 17, 17, 14, 15, 16, 16, 17, 17, 16, 17, 17, 12, 13, 14, 13, 13, 14, 14, 15, 16, 16, 16, 16, 18, 17, 24, 17, 21, 21, 18, 21

Offset: 3

Author

Rémy Sigrist, Oct 18 2017

Keywords

• nonn
• look

Comments

The scatterplot of this sequence has interesting features, such as rectangular clusters of points.

For any n > 2, A229037(n) <= a(n) + 1, with equality for n=3, 6, 8, 24 (and possibly no other values).

Examples

			For n=7: A229037(7) must be distinct from:
- 2*A229037(7-1) - A229037(7-2) = 2*2 - 1 = 3,
- 2*A229037(7-2) - A229037(7-4) = 2*1 - 2 = 2,
- 2*A229037(7-3) - A229037(7-6) = 2*1 - 1 = 1.
Hence a(7) = 3.
		

Links

• Rémy Sigrist, Table of n, a(n) for n = 3..10000
• Rémy Sigrist, Scatterplot of the first 100000 terms
• Rémy Sigrist, C++ program for A293866

Crossrefs

Cf. A229037.

Formula

a(n) = max_{j=1..floor((n-1)/2)} (2*A229037(n-j) - A229037(n-2*j)).