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A295277 a(n) = number of distinct earlier terms that have no common one bit with n in binary representation. 3
0, 1, 1, 2, 2, 2, 1, 3, 2, 2, 1, 4, 2, 2, 1, 5, 3, 4, 2, 4, 2, 2, 1, 6, 4, 4, 2, 4, 2, 2, 1, 7, 4, 4, 2, 4, 2, 2, 1, 8, 4, 4, 2, 4, 2, 2, 1, 9, 5, 6, 3, 6, 3, 4, 2, 8, 4, 4, 2, 4, 2, 2, 1, 10, 6, 6, 3, 7, 4, 4, 2, 8, 4, 4, 2, 4, 2, 2, 1, 11, 6, 6, 3, 8, 4, 4 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,4

COMMENTS

This sequence is a variant of A295276: here we count earlier terms without multiplicity, there with multiplicity.

The scatterplot of the first terms has fractal features (see scatterplot in Links section); see also A295283 for a variant of this sequence.

LINKS

Rémy Sigrist, Table of n, a(n) for n = 1..25000

Rémy Sigrist, Scatterplot of the first 2^20 terms

Rémy Sigrist, Colored scatterplot of the first 2^20 terms (where the color is function of min(A000120(a(n)), A000120((Max_{k=1..n-1} a(k))+1-a(n))))

FORMULA

a(n) = #{ a(k) such that 0 < k < n and a(k) AND n = 0 } (where AND stands for the bitwise AND operator).

EXAMPLE

The first terms, alongside the distinct earlier terms with no common one bit with n, are:

  n   a(n)    Distinct earlier terms with no common one bit with n

  --  ----    ----------------------------------------------------

   1     0    {}

   2     1    {0}

   3     1    {0}

   4     2    {0, 1}

   5     2    {0, 2}

   6     2    {0, 1}

   7     1    {0}

   8     3    {0, 1, 2}

   9     2    {0, 2}

  10     2    {0, 1}

  11     1    {0}

  12     4    {0, 1, 2, 3}

  13     2    {0, 2}

  14     2    {0, 1}

  15     1    {0}

  16     5    {0, 1, 2, 3, 4}

  17     3    {0, 2, 4}

  18     4    {0, 1, 4, 5}

  19     2    {0, 4}

  20     4    {0, 1, 2, 3}

PROG

(PARI) mx=-1; for (n=1, 86, v=sum(i=0, mx, bitand(i, n)==0); print1(v ", "); mx=max(mx, v))

CROSSREFS

Cf. A000120, A295276, A295283.

Sequence in context: A078687 A133138 A194326 * A194290 A257079 A260372

Adjacent sequences:  A295274 A295275 A295276 * A295278 A295279 A295280

KEYWORD

nonn,base

AUTHOR

Rémy Sigrist, Nov 19 2017

STATUS

approved

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Last modified June 19 19:03 EDT 2019. Contains 324222 sequences. (Running on oeis4.)