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A297252
Numbers whose base-4 digits have greater down-variation than up-variation; see Comments.
4
4, 8, 9, 12, 13, 14, 16, 20, 24, 28, 32, 33, 36, 37, 40, 41, 44, 45, 48, 49, 50, 52, 53, 54, 56, 57, 58, 60, 61, 62, 64, 68, 72, 76, 80, 84, 88, 92, 96, 100, 104, 108, 112, 116, 120, 124, 128, 129, 132, 133, 136, 137, 140, 141, 144, 145, 148, 149, 152, 153
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
153 in base-4: 2,1,2,1, having DV = 2, UV = 1, so that 153 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