

A297258


Numbers whose base6 digits have greater downvariation than upvariation; see Comments.


4



6, 12, 13, 18, 19, 20, 24, 25, 26, 27, 30, 31, 32, 33, 34, 36, 42, 48, 54, 60, 66, 72, 73, 78, 79, 84, 85, 90, 91, 96, 97, 102, 103, 108, 109, 110, 114, 115, 116, 120, 121, 122, 126, 127, 128, 132, 133, 134, 138, 139, 140, 144, 145, 146, 147, 150, 151, 152
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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

152 in base6: 4,1,2, having DV = 3, UV = 1, so that 152 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 = 6; 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] (* A297258 *)
Take[Flatten[Position[w, 0]], 120] (* A297259 *)
Take[Flatten[Position[w, 1]], 120] (* A297260 *)


CROSSREFS

Cf. A297330, A297259, A297260.
Sequence in context: A004749 A107687 A337480 * A296702 A297135 A004758
Adjacent sequences: A297255 A297256 A297257 * A297259 A297260 A297261


KEYWORD

nonn,base,easy


AUTHOR

Clark Kimberling, Jan 15 2018


STATUS

approved



