A367091 Length of runs of consecutive numbers in A367090, i.e., size of gaps in the set of sums of distinct powers of 3 and distinct powers of 4.

2, 2, 36, 36, 2, 2, 23, 2, 2, 36, 36, 2, 2, 23, 2, 2, 36, 2, 2, 36, 2, 2, 23, 2, 2, 36, 36, 2, 2, 23, 2, 2, 2, 2, 2, 2, 23, 2, 2, 36, 36, 2, 2, 23, 2, 2, 36, 2, 2, 14, 14, 2, 2, 36, 2, 2, 23, 2, 2, 36, 36, 2, 2, 23, 2, 2, 2, 2, 2, 2, 23, 2, 2, 36, 36, 2, 2, 23, 2, 2, 36, 2, 2, 36

Offset: 1

Author

M. F. Hasler, Nov 08 2023

Keywords

• nonn

Comments

The numbers that occur in this sequence are, in order of first appearance: 2, 36, 23, 14, 1081, 20, ... It is not known which numbers will eventually appear and which numbers will never occur in this sequence.

The first 1's (which correspond to isolated numbers in A367090, or gaps that are a singleton) appear as a(131) = a(132) = 1.

This set exhibits an interesting self-similar, pseudo-symmetric structure. This is due to the Proposition given in A367090.

Examples

			Sequence A367090 (= numbers that are not the sum of distinct powers of 3 or 4) starts (62, 63, 143, 144, 207, 208, 209, 210, ...), so the first two runs of consecutive terms are 2 = #{62, 63} and 2 = #{143, 144}, the next run is of length 36.
		

Links

• Hugo Pfoertner, Table of n, a(n) for n = 1..10000

Crossrefs

Cf. A367090; A005836 and A000695 (sums of distinct powers of 3 resp. 4).

Programs

PARI

D(v)=v[^1]-v[^-1] \\ first differences
A367091_upto(N, DA=D(A367090_upto(N)))= D([ k | k<-[0..#DA], !k|| DA[k]-1 ])