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A297288
Numbers whose base-16 digits have greater down-variation than up-variation; see Comments.
4
16, 32, 33, 48, 49, 50, 64, 65, 66, 67, 80, 81, 82, 83, 84, 96, 97, 98, 99, 100, 101, 112, 113, 114, 115, 116, 117, 118, 128, 129, 130, 131, 132, 133, 134, 135, 144, 145, 146, 147, 148, 149, 150, 151, 152, 160, 161, 162, 163, 164, 165, 166, 167, 168, 169
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.
Differs from A296761 first at 288 = 120_16, which has the same number of rises and falls (so not in A296761) but DV =2 > UV =1 (so in this sequence). - R. J. Mathar, Jan 23 2018
LINKS
EXAMPLE
169 in base-16: 10,9 having DV = 1, UV = 0, so that 169 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 = 16; 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] (* A297288 *)
Take[Flatten[Position[w, 0]], 120] (* A297289 *)
Take[Flatten[Position[w, 1]], 120] (* A297290 *)
CROSSREFS
KEYWORD
nonn,base,easy
AUTHOR
Clark Kimberling, Jan 17 2018
STATUS
approved