A297255 - OEIS

A297255

Numbers whose base-5 digits have greater down-variation than up-variation; see Comments.

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

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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

123 in base-5: 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 *)