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

Author

Clark Kimberling, Jan 16 2018

Keywords

• nonn
• base
• easy

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

Examples

			521 in base-11:  4,3,4, having DV = 1, UV = 1, so that 521 is in the sequence.
		

Links

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

Crossrefs

Cf. A297330, A297273, A297275.

Programs

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 *)