A297263 - OEIS

A297263

Numbers whose base-7 digits have greater up-variation than down-variation; see Comments.

9, 10, 11, 12, 13, 17, 18, 19, 20, 25, 26, 27, 33, 34, 41, 51, 52, 53, 54, 55, 58, 59, 60, 61, 62, 65, 66, 67, 68, 69, 72, 73, 74, 75, 76, 79, 80, 81, 82, 83, 86, 87, 88, 89, 90, 93, 94, 95, 96, 97, 101, 102, 103, 104, 108, 109, 110, 111, 115, 116, 117, 118

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OFFSET

1,1

COMMENTS

Suppose that n has base-b digits b(m), b(m-1), ..., b(0). The base-b down-variation of n is the sum DV(n,b) of all d(i)-d(i-1) for which d(i) > d(i-1); the base-b up-variation of n is the sum UV(n,b) of all d(k-1)-d(k) for which d(k) < d(k-1). The total base-b 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

118 in base-7: 2,2,6, having DV = 0, UV = 4, so that 118 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 = 7; 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] (* A297261 *)

Take[Flatten[Position[w, 0]], 120] (* A297262 *)

Take[Flatten[Position[w, 1]], 120] (* A297263 *)