A032841 - OEIS

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A032841

Numbers whose base-3 representation Sum_{i=0..m} d(i)*3^i has d(m) < d(m-1) > d(m-2) < ...

1, 2, 5, 15, 16, 46, 47, 50, 138, 141, 142, 150, 151, 415, 416, 424, 425, 428, 451, 452, 455, 1245, 1248, 1249, 1272, 1275, 1276, 1284, 1285, 1353, 1356, 1357, 1365, 1366, 3736, 3737, 3745, 3746, 3749, 3817, 3818, 3826, 3827

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

OFFSET

1,2

COMMENTS

For any a(n) == 0 (mod 3), 3*a(n)+1 and 3*a(n)+2 are also in the sequence, but 3*a(n) is not. Likewise, for any a(n) == 2 (mod 3) -- except for a(2)=2 -- 3*a(n) and 3*a(n)+1 are in the sequence but 3*a(n)+2 is not. - Christian N. K. Anderson, May 21 2024

LINKS

Christian N. K. Anderson, Table of n, a(n) for n = 1..10000

EXAMPLE

The numbers {415, 416, 424, 425, 428, 451, 452, 455} are in the sequence because in base 3 they are {120101, 120102, 120201, 120202, 120212, 121201, 121202, 121212}; all the six-digit base-3 numbers that fit the pattern. - Christian N. K. Anderson, May 21 2024

PROG

(R)

updown.base<-function(base, ndig, curdig=1, diglist=rep(NA, ndig)) {

if(curdig>ndig) return(sum(base^(ndig:1-1)*diglist)); nextstep<-function(i) {diglist[curdig]=i; updown.base(base, ndig, curdig+1, diglist)}; if(curdig==1) return(sort(unlist(sapply(1:(base-2+(ndig==1)), nextstep)))); if(curdig%%2) return(sapply((diglist[curdig-1]-1):0, nextstep)); sapply((diglist[curdig-1]+1):(base-1), nextstep) }; sapply(1:10, function(nd) updown.base(3, nd)) # Christian N. K. Anderson, May 21 2024

CROSSREFS

Cf. A032850 for digits <= or >= previous digit (also in base 3).

Cf. A032842 for same sequence in base 4, A032843 base 5, A032844 base 6, A032845 base 7, A032846 base 8, A032847 base 9, A032848 base 10, and A032849 base 2.

Sequence in context: A336385 A146109 A146108 * A058221 A349734 A146122

Adjacent sequences: A032838 A032839 A032840 * A032842 A032843 A032844

KEYWORD

nonn,base

AUTHOR

Clark Kimberling

STATUS

approved