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A297284 Numbers whose base-14 digits have greater up-variation than down-variation; see Comments. 4
16, 17, 18, 19, 20, 21, 22, 23, 24, 25, 26, 27, 31, 32, 33, 34, 35, 36, 37, 38, 39, 40, 41, 46, 47, 48, 49, 50, 51, 52, 53, 54, 55, 61, 62, 63, 64, 65, 66, 67, 68, 69, 76, 77, 78, 79, 80, 81, 82, 83, 91, 92, 93, 94, 95, 96, 97, 106, 107, 108, 109, 110, 111 (list; graph; refs; listen; history; text; internal format)
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 A296754 first at 198 =102_14, which is in this sequence because UV(102,14) = 2 > DV(102,14) =1, but has the same number of rises and falls and is not in A296754. - R. J. Mathar, Jan 23 2018
LINKS
EXAMPLE
111 in base-14: 7,13 having DV = 0, UV = 6, so that 111 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 = 14; 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] (* A297282 *)
Take[Flatten[Position[w, 0]], 120] (* A297283 *)
Take[Flatten[Position[w, 1]], 120] (* A297284 *)
CROSSREFS
Sequence in context: A115420 A250038 A296754 * A270043 A209726 A326455
KEYWORD
nonn,base,easy
AUTHOR
Clark Kimberling, Jan 17 2018
STATUS
approved

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Last modified February 21 04:08 EST 2024. Contains 370219 sequences. (Running on oeis4.)