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A297254
Numbers whose base-4 digits have greater up-variation than down-variation; see Comments.
4
6, 7, 11, 18, 19, 22, 23, 26, 27, 30, 31, 35, 39, 43, 47, 66, 67, 70, 71, 74, 75, 78, 79, 82, 83, 86, 87, 90, 91, 94, 95, 98, 99, 102, 103, 106, 107, 110, 111, 114, 115, 118, 119, 122, 123, 126, 127, 131, 135, 139, 143, 147, 151, 155, 159, 163, 167, 171, 175
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
EXAMPLE
175 in base-4: 2,2,3,3, having DV = 0, UV = 1, so that 175 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 = 4; 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] (* A297252 *)
Take[Flatten[Position[w, 0]], 120] (* A297253 *)
Take[Flatten[Position[w, 1]], 120] (* A297254 *)
CROSSREFS
KEYWORD
nonn,base,easy
AUTHOR
Clark Kimberling, Jan 15 2018
STATUS
approved