

A297280


Numbers whose base13 digits have equal downvariation and upvariation; see Comments.


4



1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 14, 28, 42, 56, 70, 84, 98, 112, 126, 140, 154, 168, 170, 183, 196, 209, 222, 235, 248, 261, 274, 287, 300, 313, 326, 340, 353, 366, 379, 392, 405, 418, 431, 444, 457, 470, 483, 496, 510, 523, 536, 549, 562, 575, 588
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OFFSET

1,2


COMMENTS

Suppose that n has baseb digits b(m), b(m1), ..., b(0). The baseb downvariation of n is the sum DV(n,b) of all d(i)d(i1) for which d(i) > d(i1); the baseb upvariation of n is the sum UV(n,b) of all d(k1)d(k) for which d(k) < d(k1). The total baseb 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 A029958 first for 2211 = 1011_13, which is not a palindrome in base 13 but has DV(2211,13) = UV(2211,13) =1.  R. J. Mathar, Jan 23 2018


LINKS

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


EXAMPLE

588 in base13: 3,6,3, having DV = 3, UV = 3, so that 588 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 = 13; 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] (* A297279 *)
Take[Flatten[Position[w, 0]], 120] (* A297280 *)
Take[Flatten[Position[w, 1]], 120] (* A297281 *)


CROSSREFS

Cf. A297330, A297279, A297281.
Sequence in context: A043716 A296750 A029958 * A048324 A048337 A003964
Adjacent sequences: A297277 A297278 A297279 * A297281 A297282 A297283


KEYWORD

nonn,base,easy


AUTHOR

Clark Kimberling, Jan 17 2018


STATUS

approved



