A327460 Lexicographically earliest infinite sequence of distinct positive integers such that for every k >= 1, all the k(k+1)/2 numbers in the triangle of differences of the first k terms are distinct.

1, 3, 9, 5, 12, 10, 23, 8, 22, 17, 42, 16, 43, 20, 38, 26, 45, 32, 65, 28, 64, 39, 76, 34, 81, 48, 98, 40, 92, 54, 109, 60, 116, 51, 114, 58, 117, 70, 136, 67, 135, 71, 145, 72, 147, 69, 146, 80, 164, 87, 166, 82, 170, 108, 198, 101

Offset: 1

Author

N. J. A. Sloane, Sep 25 2019

Keywords

• nonn
• nice

Comments

This is an infinite version of A327762. The first 55 terms are the same as in A327762.

Inspired by A327743.

The usual topological arguments show that there IS a sequence satisfying the definition. So far, the terms of A327460 lie on two roughly straight lines, of slopes about 1.75 and 3.5: see A328069, A328070. - N. J. A. Sloane, Oct 07 2019

If only the first differences are constrained, one gets the classical Mian-Chowla sequence A005282. - M. F. Hasler, Oct 09 2019. See also another classic, A005228, and A328190. - N. J. A. Sloane, Nov 01 2019

Examples

			The difference triangle of the first k=8 terms of the sequence is
     1,    3,    9,   5,  12,  10,  23, 8, ...
     2,    6,   -4,   7,  -2,  13, -15, ...
     4,  -10,   11,  -9,  15, -28, ...
   -14,   21,  -20,  24, -43, ...
    35,  -41,   44, -67, ...
   -76,   85, -111, ...
   161, -196, ...
  -357, ...
All 8*9/2 = 36 numbers are distinct.
		

Links

• Peter Kagey, Table of n, a(n) for n = 1..4000

Crossrefs

Cf. A005228, A005282, A035313, A327743, A327762, A328190.

See also A327458 (differences), A328066 (sorted), A328067, A328068 (complement), A328069 and A328070 (bisections), A328071; A235538 (absolute differences distinct).

The inverse binomial transform is A327459.