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A329873 a(n) is the number of distinct prime numbers whose binary digits appear in order but not necessarily as consecutive digits in the binary representation of n. 2
0, 0, 1, 1, 1, 3, 2, 2, 1, 3, 3, 5, 2, 5, 3, 2, 1, 4, 3, 6, 3, 6, 5, 6, 2, 5, 5, 6, 3, 6, 3, 3, 1, 4, 4, 7, 3, 9, 6, 7, 3, 8, 6, 9, 5, 8, 6, 8, 2, 6, 5, 7, 5, 8, 6, 8, 3, 6, 6, 9, 3, 8, 4, 3, 1, 4, 4, 8, 4, 9, 7, 9, 3, 11, 9, 11, 6, 11, 7, 10, 3, 8, 8, 12, 6 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,6

COMMENTS

This sequence is unbounded.

LINKS

Rémy Sigrist, Table of n, a(n) for n = 0..16384

FORMULA

A078826(n) <= a(n) <= A007306(n+1).

a(2*n) = a(n) + A036987(n) for any n > 0.

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

EXAMPLE

The first terms, alongside the binary representations of n and of the corresponding prime numbers, are:

  n   a(n)  bin(n)  {bin(p)}

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

   0     0       0  {}

   1     0       1  {}

   2     1      10  {10}

   3     1      11  {11}

   4     1     100  {10}

   5     3     101  {10, 11, 101}

   6     2     110  {10, 11}

   7     2     111  {11, 111}

   8     1    1000  {10}

   9     3    1001  {10, 11, 101}

  10     3    1010  {10, 11, 101}

  11     5    1011  {10, 11, 101, 111, 1011}

  12     2    1100  {10, 11}

PROG

(PARI) a(n, base=2) = { my (b=digits(n, base), s=[0]); for (k=1, #b, s = setunion(s, apply(o -> base*o+b[k], s))); #select(isprime, s) }

CROSSREFS

Cf. A007306, A036987, A078826, A303077.

Sequence in context: A171900 A204257 A074976 * A068448 A054081 A164585

Adjacent sequences:  A329870 A329871 A329872 * A329874 A329875 A329876

KEYWORD

nonn,look,base

AUTHOR

Rémy Sigrist, Nov 23 2019

STATUS

approved

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Last modified February 23 00:28 EST 2020. Contains 332157 sequences. (Running on oeis4.)