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A295276 a(n) = number of earlier terms (with multiplicity) that have no common one bit with n in binary representation. 2
0, 1, 1, 3, 1, 4, 1, 7, 2, 6, 2, 8, 3, 5, 1, 15, 6, 9, 3, 13, 4, 8, 3, 18, 7, 9, 3, 13, 3, 6, 1, 31, 11, 16, 6, 22, 7, 12, 4, 29, 13, 12, 5, 17, 5, 9, 2, 41, 15, 23, 8, 23, 7, 13, 4, 31, 12, 14, 5, 16, 4, 7, 1, 63, 24, 36, 16, 31, 12, 20, 8, 45, 20, 24, 12, 22 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,4

COMMENTS

This sequence is a binary variant of A096216: here we check for common one bits and there for common prime factors.

LINKS

Rémy Sigrist, Table of n, a(n) for n = 1..8192

Rémy Sigrist, Colored scatterplot of the first 2^15 terms (where the color is function of the Hamming weight of n)

FORMULA

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

a(2^n) = 2^n-1 for any n > 0.

a(2^n-1) = 1 for any n > 1.

EXAMPLE

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

  n   a(n)    Earlier terms with no common one bit with n

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

   1     0    ()

   2     1    (0)

   3     1    (0)

   4     3    (0, 1, 1)

   5     1    (0)

   6     4    (0, 1, 1, 1)

   7     1    (0)

   8     7    (0, 1, 1, 3, 1, 4, 1)

   9     2    (0, 4)

  10     6    (0, 1, 1, 1, 4, 1)

  11     2    (0, 4)

  12     8    (0, 1, 1, 3, 1, 1, 2, 2)

  13     3    (0, 2, 2)

  14     5    (0, 1, 1, 1, 1)

  15     1    (0)

  16    15    (0, 1, 1, 3, 1, 4, 1, 7, 2, 6, 2, 8, 3, 5, 1)

  17     6    (0, 4, 2, 6, 2, 8)

  18     9    (0, 1, 1, 1, 4, 1, 8, 5, 1)

  19     3    (0, 4, 8)

  20    13    (0, 1, 1, 3, 1, 1, 2, 2, 8, 3, 1, 9, 3)

PROG

(PARI) a = vector(76); for(n=1, #a, a[n] = sum(i=1, n-1, bitand(a[i], n)==0); print1(a[n] ", "))

CROSSREFS

Cf. A096216.

Sequence in context: A094119 A210622 A335113 * A301856 A301829 A006022

Adjacent sequences:  A295273 A295274 A295275 * A295277 A295278 A295279

KEYWORD

nonn,base

AUTHOR

Rémy Sigrist, Nov 19 2017

STATUS

approved

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Last modified September 17 19:58 EDT 2021. Contains 347489 sequences. (Running on oeis4.)