[seqfan] Plot Of A160855

Leroy Quet q1qq2qqq3qqqq at yahoo.com
Sun Jul 5 20:25:39 CEST 2009

A160855 is:
a(n) = the smallest positive integer not occurring earlier in the sequence such that sum{k=1 to n} a(k) written in binary contains binary n as a substring.

(1, 3, 2, 6, 8, 4, 5, 11, 10, 24, 12, 13, 7, 9, 28, 17, 36, 14, 20, 46,...)

Now, after Ray Chandler, I think it was, extended this sequence out for many terms, its scatter-plot was at that point rather interesting, in my opinion.

But now that H. v. Eitzen has extended the sequence out to 100000 terms, the scatter-plot is even more interesting.

What explains the radiating lines, or explains the seeming random blobs seen when the scatter-plot is taken to a smaller number of terms?

I must be missing something obvious as to why these structures occur. What kinds of structures are seen when the plot is taken even farther out, I wonder?

Leroy Quet


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