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 A044140 Numbers k such that substring "02" occurs in the base-7 representation of k but not of k-1. 0

%I #18 May 20 2019 07:11:07

%S 51,100,149,198,247,296,345,357,394,443,492,541,590,639,688,700,737,

%T 786,835,884,933,982,1031,1043,1080,1129,1178,1227,1276,1325,1374,

%U 1386,1423,1472,1521,1570,1619,1668,1717,1729,1766,1815

%N Numbers k such that substring "02" occurs in the base-7 representation of k but not of k-1.

%F Conjectures from _Colin Barker_, May 20 2019: (Start)

%F G.f.: x*(51 + 49*x + 49*x^2 + 49*x^3 + 49*x^4 + 49*x^5 + 49*x^6 + 12*x^7 - 14*x^8) / ((1 - x)^2*(1 + x)*(1 + x^2)*(1 + x^4)).

%F a(n) = a(n-1) + a(n-8) - a(n-9) for n>9.

%F (End)

%t okQ[n_]:=MemberQ[Partition[IntegerDigits[n,7],2,1],{0,2}] && !MemberQ[Partition[IntegerDigits[n-1,7],2,1],{0,2}]; Select[Range[2000],okQ] (* _Harvey P. Dale_, Feb 02 2011 *)

%t SequencePosition[Table[If[SequenceCount[IntegerDigits[n,7],{0,2}]>0,1,0],{n,2000}],{0,1}][[All,2]] (* Requires Mathematica version 10 or later *) (* _Harvey P. Dale_, Jul 09 2018 *)

%Y Cf. A007093 (numbers in base 7).

%K nonn,base

%O 1,1

%A _Clark Kimberling_

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Last modified June 20 11:48 EDT 2024. Contains 373527 sequences. (Running on oeis4.)