

A297255


Numbers whose base5 digits have greater downvariation than upvariation; see Comments.


4



5, 10, 11, 15, 16, 17, 20, 21, 22, 23, 25, 30, 35, 40, 45, 50, 51, 55, 56, 60, 61, 65, 66, 70, 71, 75, 76, 77, 80, 81, 82, 85, 86, 87, 90, 91, 92, 95, 96, 97, 100, 101, 102, 103, 105, 106, 107, 108, 110, 111, 112, 113, 115, 116, 117, 118, 120, 121, 122, 123
(list;
graph;
refs;
listen;
history;
text;
internal format)



OFFSET

1,1


COMMENTS

Suppose that n has baseb digits b(m), b(m1), ..., b(0). The baseb downvariation of n is the sum DV(n,b) of all d(i)d(i1) for which d(i) > d(i1); the baseb upvariation of n is the sum UV(n,b) of all d(k1)d(k) for which d(k) < d(k1). The total baseb variation of n is the sum TV(n,b) = DV(n,b) + UV(n,b). See the guide at A297330.


LINKS

Clark Kimberling, Table of n, a(n) for n = 1..10000


EXAMPLE

123 in base5: 4,4,3, having DV = 1, UV = 0, so that 123 is in the sequence.


MATHEMATICA

g[n_, b_] := Map[Total, GatherBy[Differences[IntegerDigits[n, b]], Sign]];
x[n_, b_] := Select[g[n, b], # < 0 &]; y[n_, b_] := Select[g[n, b], # > 0 &];
b = 5; z = 2000; p = Table[x[n, b], {n, 1, z}]; q = Table[y[n, b], {n, 1, z}];
w = Sign[Flatten[p /. {} > {0}] + Flatten[q /. {} > {0}]];
Take[Flatten[Position[w, 1]], 120] (* A297255 *)
Take[Flatten[Position[w, 0]], 120] (* A297256 *)
Take[Flatten[Position[w, 1]], 120] (* A297257 *)


CROSSREFS

Cf. A297330, A297256, A297257.
Sequence in context: A116033 A290469 A140507 * A296699 A297132 A136823
Adjacent sequences: A297252 A297253 A297254 * A297256 A297257 A297258


KEYWORD

nonn,base,easy


AUTHOR

Clark Kimberling, Jan 15 2018


STATUS

approved



