A297261 Numbers whose base-7 digits have greater up-variation than down-variation; see Comments.

7, 14, 15, 21, 22, 23, 28, 29, 30, 31, 35, 36, 37, 38, 39, 42, 43, 44, 45, 46, 47, 49, 56, 63, 70, 77, 84, 91, 98, 99, 105, 106, 112, 113, 119, 120, 126, 127, 133, 134, 140, 141, 147, 148, 149, 154, 155, 156, 161, 162, 163, 168, 169, 170, 175, 176, 177, 182

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

Clark Kimberling, Table of n, a(n) for n = 1..10000

Example

182 in base-7:  3,5,0, having DV = 7, UV = 0, so that 182 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 = 7; 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]   (* A297261 *)
Take[Flatten[Position[w, 0]], 120]    (* A297262 *)
Take[Flatten[Position[w, 1]], 120]    (* A297263 *)

Crossrefs

Cf. A297330, A297262, A297263.

Sequence in context: A107976 A022557 A307546 * A296705 A297138 A085335

Adjacent sequences: A297258 A297259 A297260 * A297262 A297263 A297264

Keyword

nonn,base,easy

Author

Clark Kimberling, Jan 15 2018

Status

approved