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A367091
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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.
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2
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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
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OFFSET
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1,1
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COMMENTS
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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.
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LINKS
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EXAMPLE
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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.
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PROG
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(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 ])
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CROSSREFS
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KEYWORD
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nonn
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AUTHOR
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STATUS
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approved
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