A266140 -id:A266140 - cp's OEIS frontend

A297271 Numbers whose base-10 digits have equal down-variation and up-variation; see Comments.

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

Offset: 1

Clark Kimberling, Jan 16 2018

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

			13601 in base-10:  1,3,6,0,1, having DV = 6, UV = 6, so that 13601 is in the sequence.

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

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

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 *)

{k: A037851(k) = A037860(k)}. - R. J. Mathar, Sep 27 2021

A266280 Terms in A083115 that are the smallest members of equivalence classes generated by permutation of digits.

Original entry on oeis.org

1, 2, 3, 4, 5, 6, 7, 8, 9, 11, 22, 33, 111, 121, 131, 141, 151, 161, 171, 191, 212, 222, 313, 1111, 1221, 1331, 11111, 11211, 11311, 11411, 11511, 11711, 12121, 12221, 13131, 111111, 112211, 1111111, 1112111, 1113111, 1115111, 1121211, 1131311, 11111111, 111111111

Offset: 1

Chai Wah Wu, Dec 27 2015

Subsequence of A083115. Intersection of A083114 and A266140.

Differs from A083115 first at n=27.

Chai Wah Wu, Table of n, a(n) for n = 1..132

Cf. A083114, A083115, A266140.

cp's OEIS Frontend

A297271 Numbers whose base-10 digits have equal down-variation and up-variation; see Comments.

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