A031941 Numbers without consecutive equal base 3 digits.

1, 2, 3, 5, 6, 7, 10, 11, 15, 16, 19, 20, 21, 23, 30, 32, 33, 34, 46, 47, 48, 50, 57, 59, 60, 61, 64, 65, 69, 70, 91, 92, 96, 97, 100, 101, 102, 104, 138, 140, 141, 142, 145, 146, 150, 151, 172, 173, 177, 178, 181, 182, 183, 185, 192

Offset

1,2

Comments

Essentially the same as A043089, b.t.w. the initial "0" could be as well included here. Also: numbers k such that A043277(k)=1. - M. F. Hasler, Jul 23 2013

There are 2^k terms having k digits in base 3, k > 0. - David A. Corneth, Sep 09 2025

Links

David A. Corneth, Table of n, a(n) for n = 1..16382

Formula

A031941 = { n | A043277(n)=1 } = A043089 \ {0}. - M. F. Hasler, Jul 23 2013

Mathematica

Select[Range[200], FreeQ[Differences[IntegerDigits[#, 3]], 0]&] (* Harvey P. Dale, Mar 03 2024 *)

Prog

(PARI) for(i=1, 199, A043277(i)==1 & print1(i", ")) \\ M. F. Hasler, Jul 23 2013
(PARI) a(n) = {if(n==0, return(0)); n++; my(b=binary(n), ld=0); b[1] = 0; for(i=2, #b, b[i] = b[i]+=(b[i-1]<=b[i])); fromdigits(b, 3)} \\ David A. Corneth, Sep 09 2025
(PARI) uptoqternarydigits(n) = {maxqd = n; res = List(); process(0, 0); listpop(res, 1); Set(res)}
process(n, qd) = {listput(res, n); if(qd >= maxqd, return); my(r = n%3); for(i = 0, 2, if(r != i, process(3*n + i, qd + 1)))}

Crossrefs

Cf. A000975 (base-2 analog), A031942 or A043090 (base-4 analog), A031943 or A043091 (base-5 analog), A043092, ..., A043096 (base-6 through base-10 analog).

Sequence in context: A302597 A240101 A032892 * A043089 A088952 A303541

Adjacent sequences: A031938 A031939 A031940 * A031942 A031943 A031944

Keyword

nonn,easy,base

Author

Clark Kimberling

Extensions

Edited by Charles R Greathouse IV, Aug 02 2010

Status

approved