A297274 Numbers whose base-11 digits have equal down-variation and up-variation; see Comments.

1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 12, 24, 36, 48, 60, 72, 84, 96, 108, 120, 122, 133, 144, 155, 166, 177, 188, 199, 210, 221, 232, 244, 255, 266, 277, 288, 299, 310, 321, 332, 343, 354, 366, 377, 388, 399, 410, 421, 432, 443, 454, 465, 476, 488, 499, 510, 521

Offset

1,2

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 after the zero from A029956 first at 1343 = 1011_11, which is not a palindrome in base 11 but has DV(1343,11) = UV(1343,11) =1. - R. J. Mathar, Jan 23 2018

Links

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

Example

521 in base-11:  4,3,4, having DV = 1, UV = 1, so that 521 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 = 11; 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]   (* A297273 *)
Take[Flatten[Position[w, 0]], 120]    (* A297274 *)
Take[Flatten[Position[w, 1]], 120]    (* A297275 *)

Crossrefs

Cf. A297330, A297273, A297275.

Sequence in context: A043714 A296744 A029956 * A048322 A048335 A068862

Adjacent sequences: A297271 A297272 A297273 * A297275 A297276 A297277

Keyword

nonn,base,easy

Author

Clark Kimberling, Jan 16 2018

Status

approved