login
The OEIS Foundation is supported by donations from users of the OEIS and by a grant from the Simons Foundation.

 

Logo


Hints
(Greetings from The On-Line Encyclopedia of Integer Sequences!)
A297277 Numbers whose base-12 digits have equal down-variation and up-variation; see Comments. 4
1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 13, 26, 39, 52, 65, 78, 91, 104, 117, 130, 143, 145, 157, 169, 181, 193, 205, 217, 229, 241, 253, 265, 277, 290, 302, 314, 326, 338, 350, 362, 374, 386, 398, 410, 422, 435, 447, 459, 471, 483, 495, 507, 519, 531, 543, 555 (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 first from A029957 after the zero for 1741 = 1011_12, which is not a palindrome in base 12 but has DV(1741,12) = UV(1741,12) =1. - R. J. Mathar, Jan 23 2018

LINKS

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

EXAMPLE

555 in base-12:  3,10,3, having DV = 7, UV = 7, so that 555 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 = 12; 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]   (* A297276 *)

Take[Flatten[Position[w, 0]], 120]    (* A297277 *)

Take[Flatten[Position[w, 1]], 120]    (* A297278 *)

CROSSREFS

Cf. A297330, A297276, A297278.

Sequence in context: A043715 A296747 A029957 * A048323 A048336 A130574

Adjacent sequences:  A297274 A297275 A297276 * A297278 A297279 A297280

KEYWORD

nonn,base,easy

AUTHOR

Clark Kimberling, Jan 16 2018

STATUS

approved

Lookup | Welcome | Wiki | Register | Music | Plot 2 | Demos | Index | Browse | More | WebCam
Contribute new seq. or comment | Format | Style Sheet | Transforms | Superseeker | Recent
The OEIS Community | Maintained by The OEIS Foundation Inc.

License Agreements, Terms of Use, Privacy Policy. .

Last modified September 16 23:53 EDT 2021. Contains 347477 sequences. (Running on oeis4.)