

A297270


Numbers whose base10 digits have greater downvariation than upvariation; 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
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OFFSET

1,1


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 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 base10: 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



