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

51, 100, 149, 198, 247, 296, 345, 357, 394, 443, 492, 541, 590, 639, 688, 700, 737, 786, 835, 884, 933, 982, 1031, 1043, 1080, 1129, 1178, 1227, 1276, 1325, 1374, 1386, 1423, 1472, 1521, 1570, 1619, 1668, 1717, 1729, 1766, 1815

Offset

1,1

Links

Table of n, a(n) for n=1..42.

Formula

Conjectures from Colin Barker, May 20 2019: (Start)

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)).

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

(End)

Mathematica

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 *)
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 *)

Crossrefs

Cf. A007093 (numbers in base 7).

Sequence in context: A049328 A075894 A229274 * A044521 A160847 A260517

Adjacent sequences: A044137 A044138 A044139 * A044141 A044142 A044143

Keyword

nonn,base

Author

Clark Kimberling

Status

approved