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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.

%I A367091 #14 Dec 15 2023 16:30:38
%S A367091 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,
%T A367091 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,
%U A367091 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
%N 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.
%C A367091 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.
%C A367091 The first 1's (which correspond to isolated numbers in A367090, or gaps that are a singleton) appear as a(131) = a(132) = 1.
%C A367091 This set exhibits an interesting self-similar, pseudo-symmetric structure. This is due to the Proposition given in A367090.
%H A367091 Hugo Pfoertner, <a href="/A367091/b367091.txt">Table of n, a(n) for n = 1..10000</a>
%e A367091 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.
%o A367091 (PARI) D(v)=v[^1]-v[^-1] \\ first differences
%o A367091 A367091_upto(N, DA=D(A367090_upto(N)))= D([ k | k<-[0..#DA], !k|| DA[k]-1 ])
%Y A367091 Cf. A367090; A005836 and A000695 (sums of distinct powers of 3 resp. 4).
%K A367091 nonn
%O A367091 1,1
%A A367091 _M. F. Hasler_, Nov 08 2023