A078826 Number of distinct primes contained as binary substrings in binary representation of n.

0, 0, 1, 1, 1, 2, 2, 2, 1, 1, 2, 4, 2, 4, 3, 2, 1, 2, 1, 3, 2, 2, 4, 6, 2, 2, 4, 5, 3, 6, 3, 3, 1, 1, 2, 3, 1, 3, 3, 4, 2, 3, 2, 5, 4, 5, 6, 7, 2, 3, 2, 3, 4, 5, 5, 7, 3, 3, 6, 8, 3, 7, 4, 3, 1, 1, 1, 3, 2, 3, 3, 5, 1, 2, 3, 5, 3, 5, 4, 5, 2, 3, 3, 6, 2, 2, 5, 7, 4, 5, 5, 5, 6, 8, 7, 8, 2, 3, 3, 3, 2, 5, 3, 5, 4

Offset

0,6

Comments

A143792(n) <= a(n) for n > 0. - Reinhard Zumkeller, Sep 08 2008

For n > 1: number of primes in n-th row of A165416, lengths in n-th row of A225243. - Reinhard Zumkeller, Jul 17 2015, Aug 14 2013

Links

Reinhard Zumkeller, Table of n, a(n) for n = 0..10000

Example

n=7 -> '111' contains 2 different binary substrings which are primes: '11' (11b or b11) and '111' itself, therefore a(7)=2.

Mathematica

a[n_] := (bits = IntegerDigits[n, 2]; lg = Length[bits]; Reap[Do[If[PrimeQ[p = FromDigits[bits[[i ;; j]], 2]], Sow[p]], {i, 1, lg-1}, {j, i+1, lg}]][[2, 1]] // Union // Length); a[0] = a[1] = 0; Table[a[n], {n, 0, 104}] (* Jean-François Alcover, May 23 2013 *)

Prog

(Haskell)
a078826 n | n <= 1 = 0
          | otherwise = length $ a225243_row n
-- Reinhard Zumkeller, Aug 14 2013

Crossrefs

Cf. A004676, A035232, A078827, A078822, A007088, A001221.

Cf. A143792, A165416, A225243.

Sequence in context: A317682 A216651 A071338 * A051950 A341062 A172353

Adjacent sequences: A078823 A078824 A078825 * A078827 A078828 A078829

Keyword

nonn,base

Author

Reinhard Zumkeller, Dec 08 2002

Status

approved