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A297282 Numbers whose base-14 digits have greater down-variation than up-variation; see Comments. 4

%I #8 Jan 23 2018 20:09:33

%S 14,28,29,42,43,44,56,57,58,59,70,71,72,73,74,84,85,86,87,88,89,98,99,

%T 100,101,102,103,104,112,113,114,115,116,117,118,119,126,127,128,129,

%U 130,131,132,133,134,140,141,142,143,144,145,146,147,148,149,154

%N Numbers whose base-14 digits have greater down-variation than up-variation; see Comments.

%C 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.

%C Differs from A296755 first for 224 = 120_14, which is in this sequence because DV(224,14) = 2 > UV(224,14)=1, but not in A296755 because the number of rises equals the number of falls. - _R. J. Mathar_, Jan 23 2018

%H Clark Kimberling, <a href="/A297282/b297282.txt">Table of n, a(n) for n = 1..10000</a>

%e 154 in base-14: 11,0 having DV = 9, UV = 0, so that 154 is in the sequence.

%t g[n_, b_] := Map[Total, GatherBy[Differences[IntegerDigits[n, b]], Sign]];

%t x[n_, b_] := Select[g[n, b], # < 0 &]; y[n_, b_] := Select[g[n, b], # > 0 &];

%t b = 14; z = 2000; p = Table[x[n, b], {n, 1, z}]; q = Table[y[n, b], {n, 1, z}];

%t w = Sign[Flatten[p /. {} -> {0}] + Flatten[q /. {} -> {0}]];

%t Take[Flatten[Position[w, -1]], 120] (* A297282 *)

%t Take[Flatten[Position[w, 0]], 120] (* A297283 *)

%t Take[Flatten[Position[w, 1]], 120] (* A297284 *)

%Y Cf. A297330, A297283, A297284.

%K nonn,base,easy

%O 1,1

%A _Clark Kimberling_, Jan 17 2018

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Last modified August 25 22:58 EDT 2024. Contains 375454 sequences. (Running on oeis4.)