This site is supported by donations to The OEIS Foundation.

 Please make a donation to keep the OEIS running. We are now in our 55th year. In the past year we added 12000 new sequences and reached 8000 citations (which often say "discovered thanks to the OEIS"). We need to raise money to hire someone to manage submissions, which would reduce the load on our editors and speed up editing. Other ways to donate

 Hints (Greetings from The On-Line Encyclopedia of Integer Sequences!)
 A297270 Numbers whose base-10 digits have greater down-variation than up-variation; see Comments. 4
 10, 20, 21, 30, 31, 32, 40, 41, 42, 43, 50, 51, 52, 53, 54, 60, 61, 62, 63, 64, 65, 70, 71, 72, 73, 74, 75, 76, 80, 81, 82, 83, 84, 85, 86, 87, 90, 91, 92, 93, 94, 95, 96, 97, 98, 100, 110, 120, 130, 140, 150, 160, 170, 180, 190, 200, 201, 210, 211, 220, 221 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,1 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 A071590 at 1101, which is in A071590, but not in here because UV(1101) = DV(1101). - R. J. Mathar, Jan 23 2018 LINKS Clark Kimberling, Table of n, a(n) for n = 1..10000 EXAMPLE 6151413121 in base-10:  6,1,5,1,4,1,3,1,2,1, having DV = 15, UV = 10, so that 6151413121 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. A297330, A297271, A297272. Sequence in context: A329480 A132782 A267759 * A071590 A210589 A296714 Adjacent sequences:  A297267 A297268 A297269 * A297271 A297272 A297273 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.

Last modified December 12 01:57 EST 2019. Contains 329948 sequences. (Running on oeis4.)