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A297269
Numbers whose base-9 digits have greater up-variation than down-variation; see Comments.
4
11, 12, 13, 14, 15, 16, 17, 21, 22, 23, 24, 25, 26, 31, 32, 33, 34, 35, 41, 42, 43, 44, 51, 52, 53, 61, 62, 71, 83, 84, 85, 86, 87, 88, 89, 92, 93, 94, 95, 96, 97, 98, 101, 102, 103, 104, 105, 106, 107, 110, 111, 112, 113, 114, 115, 116, 119, 120, 121, 122
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
122 in base-9: 1,4,5, having DV = 0, UV = 4, so that 122 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 = 9; 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] (* A297267 *)
Take[Flatten[Position[w, 0]], 120] (* A297268 *)
Take[Flatten[Position[w, 1]], 120] (* A297269 *)
CROSSREFS
KEYWORD
nonn,base,easy
AUTHOR
Clark Kimberling, Jan 15 2018
STATUS
approved