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Number of distinct primes contained as binary substrings in binary representation of n.
13

%I #11 Jul 17 2015 05:58:02

%S 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,

%T 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,

%U 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

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

%C A143792(n) <= a(n) for n > 0. - _Reinhard Zumkeller_, Sep 08 2008

%C 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

%H Reinhard Zumkeller, <a href="/A078826/b078826.txt">Table of n, a(n) for n = 0..10000</a>

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

%t 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 *)

%o (Haskell)

%o a078826 n | n <= 1 = 0

%o | otherwise = length $ a225243_row n

%o -- _Reinhard Zumkeller_, Aug 14 2013

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

%Y Cf. A143792, A165416, A225243.

%K nonn,base

%O 0,6

%A _Reinhard Zumkeller_, Dec 08 2002