login
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, 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
1,1
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.
LINKS
EXAMPLE
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.
PROG
(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 ])
CROSSREFS
Cf. A367090; A005836 and A000695 (sums of distinct powers of 3 resp. 4).
Sequence in context: A349033 A334470 A286375 * A056612 A131658 A131657
KEYWORD
nonn
AUTHOR
M. F. Hasler, Nov 08 2023
STATUS
approved