A308007 Absolute values of first differences of A081145.

1, 2, 3, 4, 5, 6, 9, 7, 8, 14, 10, 11, 18, 12, 13, 24, 15, 16, 30, 17, 19, 34, 20, 21, 39, 22, 23, 43, 25, 26, 50, 27, 28, 54, 29, 31, 57, 33, 32, 35, 36, 70, 37, 38, 73, 40, 41, 78, 42, 44, 85, 45, 46, 90, 47, 48, 94, 49, 51, 97, 52, 53, 104, 55, 56, 109, 58, 59, 116, 61, 60, 62, 63

Offset: 1

Author

N. J. A. Sloane, May 13 2019

Keywords

• nonn

Comments

The (signed) differences themselves are in A099004, but this sequence is important enough to have its own entry.

Conjectured (see the Slater-Velez and Velez articles) to be a permutation of the positive integers.

It appears that the terms line on two lines (this is true for the first million terms): see A308016-A308020.

Links

• Chai Wah Wu, Table of n, a(n) for n = 1..5000
• P. J. Slater and W. Y. Velez, Permutations of the Positive Integers with Restrictions on the Sequence of Differences, Pacific Journal of Mathematics, Vol. 71, No. 1, 1977, 193-196.
• P. J. Slater and W. Y. Velez, Permutations of the Positive Integers with Restrictions on the Sequence of Differences, II, Pacific Journal of Mathematics, Vol. 82, No. 2, 1979, 527-531.
• William Y. Velez, Research problems 159-160, Discrete Math., 110 (1992), pp. 301-302.

Crossrefs

Cf. A081145, A081146, A099004, A308021.

See also A308016-A308020.