A367091 - OEIS

The OEIS is supported by the many generous donors to the OEIS Foundation.

Year-end appeal: Please make a donation to the OEIS Foundation to support ongoing development and maintenance of the OEIS. We are now in our 61st year, we have over 378,000 sequences, and we’ve reached 11,000 citations (which often say “discovered thanks to the OEIS”).

Other ways to Give

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

(list; graph; refs; listen; history; text; internal format)

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

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

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

Adjacent sequences: A367088 A367089 A367090 * A367092 A367093 A367094

KEYWORD

nonn

AUTHOR

M. F. Hasler, Nov 08 2023

STATUS

approved