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A326781 No position of a 1 in the reversed binary expansion of n is a power of 2. 2
0, 4, 16, 20, 32, 36, 48, 52, 64, 68, 80, 84, 96, 100, 112, 116, 256, 260, 272, 276, 288, 292, 304, 308, 320, 324, 336, 340, 352, 356, 368, 372, 512, 516, 528, 532, 544, 548, 560, 564, 576, 580, 592, 596, 608, 612, 624, 628, 768, 772, 784, 788, 800, 804, 816 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,2

COMMENTS

Also BII-numbers (see A326031) of set-systems with no singleton edges. For example, the sequence of such set-systems together with their BII-numbers begins:

    0: {}

    4: {{1,2}}

   16: {{1,3}}

   20: {{1,2},{1,3}}

   32: {{2,3}}

   36: {{1,2},{2,3}}

   48: {{1,3},{2,3}}

   52: {{1,2},{1,3},{2,3}}

   64: {{1,2,3}}

   68: {{1,2},{1,2,3}}

   80: {{1,3},{1,2,3}}

   84: {{1,2},{1,3},{1,2,3}}

   96: {{2,3},{1,2,3}}

  100: {{1,2},{2,3},{1,2,3}}

  112: {{1,3},{2,3},{1,2,3}}

  116: {{1,2},{1,3},{2,3},{1,2,3}}

  256: {{1,4}}

  260: {{1,2},{1,4}}

  272: {{1,3},{1,4}}

  276: {{1,2},{1,3},{1,4}}

LINKS

Table of n, a(n) for n=1..55.

FORMULA

Conjectures from Colin Barker, Jul 27 2019: (Start)

G.f.: 4*x^2*(1 + 3*x + x^2 + 3*x^3 + x^4 + 3*x^5 + x^6 + 3*x^7 + x^8 + 3*x^9 + x^10 + 3*x^11 + x^12 + 3*x^13 + x^14 + 35*x^15) / ((1 - x)^2*(1 + x)*(1 + x^2)*(1 + x^4)*(1 + x^8)).

a(n) = a(n-1) + a(n-16) - a(n-17) for n>17.

(End)

EXAMPLE

The binary indices of n are row n of A048793. The sequence of terms together with their binary indices begins:

    0: {}

    4: {3}

   16: {5}

   20: {3,5}

   32: {6}

   36: {3,6}

   48: {5,6}

   52: {3,5,6}

   64: {7}

   68: {3,7}

   80: {5,7}

   84: {3,5,7}

   96: {6,7}

  100: {3,6,7}

  112: {5,6,7}

  116: {3,5,6,7}

  256: {9}

  260: {3,9}

  272: {5,9}

  276: {3,5,9}

MATHEMATICA

bpe[n_]:=Join@@Position[Reverse[IntegerDigits[n, 2]], 1];

Select[Range[100], !MemberQ[Length/@bpe/@bpe[#], 1]&]

CROSSREFS

Cf. A000120, A029931, A048793, A062289, A070939, A326031, A326782, A326788.

Sequence in context: A277887 A216033 A071966 * A326788 A039943 A193996

Adjacent sequences:  A326778 A326779 A326780 * A326782 A326783 A326784

KEYWORD

nonn,base

AUTHOR

Gus Wiseman, Jul 25 2019

STATUS

approved

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Last modified April 12 19:50 EDT 2021. Contains 342932 sequences. (Running on oeis4.)