login
A297255
Numbers whose base-5 digits have greater down-variation than up-variation; see Comments.
4
5, 10, 11, 15, 16, 17, 20, 21, 22, 23, 25, 30, 35, 40, 45, 50, 51, 55, 56, 60, 61, 65, 66, 70, 71, 75, 76, 77, 80, 81, 82, 85, 86, 87, 90, 91, 92, 95, 96, 97, 100, 101, 102, 103, 105, 106, 107, 108, 110, 111, 112, 113, 115, 116, 117, 118, 120, 121, 122, 123
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
123 in base-5: 4,4,3, having DV = 1, UV = 0, so that 123 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 = 5; 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] (* A297255 *)
Take[Flatten[Position[w, 0]], 120] (* A297256 *)
Take[Flatten[Position[w, 1]], 120] (* A297257 *)
CROSSREFS
KEYWORD
nonn,base,easy
AUTHOR
Clark Kimberling, Jan 15 2018
STATUS
approved