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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
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 (list; graph; refs; listen; history; text; internal format)
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

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Last modified November 18 04:44 EST 2019. Contains 329248 sequences. (Running on oeis4.)