

A297284


Numbers whose base14 digits have greater upvariation than downvariation; 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
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OFFSET

1,1


COMMENTS

Suppose that n has baseb digits b(m), b(m1), ..., b(0). The baseb downvariation of n is the sum DV(n,b) of all d(i)d(i1) for which d(i) > d(i1); the baseb upvariation of n is the sum UV(n,b) of all d(k1)d(k) for which d(k) < d(k1). The total baseb 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 base14: 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



KEYWORD

nonn,base,easy


AUTHOR



STATUS

approved



