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 A297286 Numbers whose base-15 digits have equal down-variation and up-variation; see Comments. 4
 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 16, 32, 48, 64, 80, 96, 112, 128, 144, 160, 176, 192, 208, 224, 226, 241, 256, 271, 286, 301, 316, 331, 346, 361, 376, 391, 406, 421, 436, 452, 467, 482, 497, 512, 527, 542, 557, 572, 587, 602, 617, 632, 647 (list; graph; refs; listen; history; text; internal format)
 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 from A029960 after the zero first for 3391 = 1011_15, which is not in A029960 but in this sequence. - R. J. Mathar, Jan 23 2018 LINKS Clark Kimberling, Table of n, a(n) for n = 1..10000 EXAMPLE 647 in base-15: 2,13,2 having DV = 11, UV = 11, so that 647 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 = 15; 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] (* A297285 *) Take[Flatten[Position[w, 0]], 120] (* A297286 *) Take[Flatten[Position[w, 1]], 120] (* A297287 *) CROSSREFS Cf. A297330, A297285, A297287. Sequence in context: A043718 A296756 A029960 * A048326 A048339 A023783 Adjacent sequences: A297283 A297284 A297285 * A297287 A297288 A297289 KEYWORD nonn,base,easy AUTHOR Clark Kimberling, Jan 17 2018 STATUS approved

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Last modified June 3 18:44 EDT 2023. Contains 363116 sequences. (Running on oeis4.)