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A297271 Numbers whose base-10 digits have equal down-variation and up-variation; see Comments. 4
1, 2, 3, 4, 5, 6, 7, 8, 9, 11, 22, 33, 44, 55, 66, 77, 88, 99, 101, 111, 121, 131, 141, 151, 161, 171, 181, 191, 202, 212, 222, 232, 242, 252, 262, 272, 282, 292, 303, 313, 323, 333, 343, 353, 363, 373, 383, 393, 404, 414, 424, 434, 444, 454, 464, 474, 484 (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 after the zero from A002113 first at 1011, which is not a palindrome but has DV(1011,10) = UV(1011,10) =1. - R. J. Mathar, Jan 23 2018

Apart from 0, the initial terms coincide with those of A266140, but the two sequences are different. First disagreement: a(109) = 1001 and A266140(110) = 1111. - Georg Fischer, Oct 09 2018

LINKS

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

EXAMPLE

13601 in base-10:  1,3,6,0,1, having DV = 6, UV = 6, so that 13601 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 = 10; 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]   (* A297270 *)

Take[Flatten[Position[w, 0]], 120]    (* A297271 *)

Take[Flatten[Position[w, 1]], 120]    (* A297272 *)

CROSSREFS

Cf. A002113, A266140, A297330, A297270, A297272.

Sequence in context: A296712 A276115 A266140 * A110751 A147882 A002113

Adjacent sequences:  A297268 A297269 A297270 * A297272 A297273 A297274

KEYWORD

nonn,base,easy

AUTHOR

Clark Kimberling, Jan 16 2018

STATUS

approved

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Last modified December 12 15:11 EST 2019. Contains 329960 sequences. (Running on oeis4.)