A072832 First differences of Ulam's sequence A002858.

1, 1, 1, 2, 2, 3, 2, 3, 2, 8, 2, 8, 2, 9, 1, 5, 4, 5, 7, 3, 5, 5, 5, 10, 2, 3, 4, 8, 12, 5, 7, 7, 3, 7, 20, 2, 3, 2, 7, 8, 9, 3, 10, 2, 15, 2, 3, 2, 10, 5, 2, 13, 9, 27, 7, 3, 5, 15, 2, 15, 2, 5, 7, 12, 8, 10, 2, 7, 3, 2, 15, 2, 3, 7, 10, 5, 27, 2, 12, 5, 20, 2, 20, 2, 20, 2, 17, 17, 3, 2, 5, 12, 3

Offset: 1

Author

N. J. A. Sloane, Jul 25 2002

Keywords

• nonn
• easy

Comments

No pattern in this sequence has ever been observed, according to Finch.

In the first 49,999,999 terms, 1 occurs four times, 36.9% of the terms are 2, and some terms have not occurred. - Jud McCranie, Mar 02 2012

Even though some values seem to get larger as the sequence grows, it appears that the combined frequency of the values 2 and 3 approaches 50%. This shows up even in the first 10000 terms (combined frequency: 49.9%). - Enrique Navarrete, May 08 2017

References

• Steven R. Finch, Mathematical Constants, Cambridge, 2003, pp. 145-151.

Links

• Jud McCranie, Table of n, a(n) for n = 1..10000
• Steven R. Finch, Stolarsky-Harborth Constant [Broken link]
• Steven R. Finch, Stolarsky-Harborth Constant [From the Wayback machine]

Crossrefs

Cf. A002858, A072540 (conjectured missing terms).

Extensions

More terms from Matthew Conroy, Aug 24 2002