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

Author

Reinhard Zumkeller, Dec 08 2002

Keywords

• nonn
• base

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

Examples

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

Links

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

Crossrefs

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

Cf. A143792, A165416, A225243.

Programs

Haskell

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

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 *)