login
This site is supported by donations to The OEIS Foundation.

 

Logo

Please make a donation to keep the OEIS running. We are now in our 55th year. In the past year we added 12000 new sequences and reached 8000 citations (which often say "discovered thanks to the OEIS"). We need to raise money to hire someone to manage submissions, which would reduce the load on our editors and speed up editing.
Other ways to donate

Hints
(Greetings from The On-Line Encyclopedia of Integer Sequences!)
A297134 Numbers having an up-first zigzag pattern in base 6; see Comments. 4
8, 9, 10, 11, 15, 16, 17, 22, 23, 29, 48, 49, 51, 52, 53, 54, 55, 56, 58, 59, 60, 61, 62, 63, 65, 66, 67, 68, 69, 70, 90, 91, 92, 94, 95, 96, 97, 98, 99, 101, 102, 103, 104, 105, 106, 132, 133, 134, 135, 137, 138, 139, 140, 141, 142, 174, 175, 176, 177, 178 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,1

COMMENTS

A number n having base-b digits d(m), d(m-1),..., d(0) such that d(i) != d(i+1) for 0 <= i < m shows a zigzag pattern of one or more segments, in the following sense.  Writing U for up and D for down, there are two kinds of patterns:  U, UD, UDU, UDUD, ... and D, DU, DUD, DUDU, ... .  In the former case, we say n has an "up-first zigzag pattern in base b"; in the latter, a "down-first zigzag pattern in base b".  Example:  2,4,5,3,0,1,4,2 has segments 2,4,5; 5,3,0; 0,1,4; and 4,2, so that 24530142, with pattern UDUD, has an up-first zigzag pattern in base 10, whereas 4,2,5,3,0,1,4,2 has a down-first pattern.  The sequences A297134-A297136 partition the natural numbers.  See the guide at A297146.

LINKS

Table of n, a(n) for n=1..60.

EXAMPLE

Base-6 digits of 5000: 3,5,0,5,2, with pattern UDUD, so that 5000 is in the sequence.

MATHEMATICA

a[n_, b_] := Sign[Differences[IntegerDigits[n, b]]]; z = 300;

b = 6; t = Table[a[n, b], {n, 1, 10*z}];

u = Select[Range[z], ! MemberQ[t[[#]], 0] && First[t[[#]]] == 1 &]   (* A297134 *)

v = Select[Range[z], ! MemberQ[t[[#]], 0] && First[t[[#]]] == -1 &]  (* A297135 *)

Complement[Range[z], Union[u, v]]  (* A297136 *)

CROSSREFS

Cf. A297135, A297136.

Sequence in context: A247631 A297260 A296701 * A247455 A280290 A138581

Adjacent sequences:  A297131 A297132 A297133 * A297135 A297136 A297137

KEYWORD

nonn,easy,base

AUTHOR

Clark Kimberling, Jan 14 2018

STATUS

approved

Lookup | Welcome | Wiki | Register | Music | Plot 2 | Demos | Index | Browse | More | WebCam
Contribute new seq. or comment | Format | Style Sheet | Transforms | Superseeker | Recent
The OEIS Community | Maintained by The OEIS Foundation Inc.

License Agreements, Terms of Use, Privacy Policy. .

Last modified December 6 21:48 EST 2019. Contains 329809 sequences. (Running on oeis4.)