

A297144


Numbers having a downfirst zigzag pattern in base 9; see Comments.


4



9, 18, 19, 27, 28, 29, 36, 37, 38, 39, 45, 46, 47, 48, 49, 54, 55, 56, 57, 58, 59, 63, 64, 65, 66, 67, 68, 69, 72, 73, 74, 75, 76, 77, 78, 79, 82, 83, 84, 85, 86, 87, 88, 89, 163, 164, 165, 166, 167, 168, 169, 170, 171, 173, 174, 175, 176, 177, 178, 179, 244
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OFFSET

1,1


COMMENTS

A number n having baseb digits d(m), d(m1),..., 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 "upfirst zigzag pattern in base b"; in the latter, a "downfirst 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 upfirst zigzag pattern in base 10, whereas 4,2,5,3,0,1,4,2 has a downfirst pattern. The sequences A297143A297145 partition the natural numbers. See the guide at A297146.


LINKS

Robert Israel, Table of n, a(n) for n = 1..10000


EXAMPLE

Base9 digits of 7280: 1,0,8,7,8, with pattern DUDU, so that 7280 is in the sequence.


MAPLE

filter:= proc(n) local L;
L:= convert(n, base, 9);
not has(L[2..1]L[1..2], 0) and L[1]>L[2]
end proc:
select(filter, [$9..1000]); # Robert Israel, Dec 06 2018


MATHEMATICA

a[n_, b_] := Sign[Differences[IntegerDigits[n, b]]]; z = 300;
b = 9; t = Table[a[n, b], {n, 1, 10*z}];
u = Select[Range[z], ! MemberQ[t[[#]], 0] && First[t[[#]]] == 1 &] (* A297143 *)
v = Select[Range[z], ! MemberQ[t[[#]], 0] && First[t[[#]]] == 1 &] (* A297144 *)
Complement[Range[z], Union[u, v]] (* A297145 *)


CROSSREFS

Cf. A297143, A297145.
Sequence in context: A060993 A297267 A296711 * A107977 A257226 A092457
Adjacent sequences: A297141 A297142 A297143 * A297145 A297146 A297147


KEYWORD

nonn,easy,base


AUTHOR

Clark Kimberling, Jan 15 2018


STATUS

approved



