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A078826 Number of distinct primes contained as binary substrings in binary representation of n. 13
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 (list; graph; refs; listen; history; text; internal format)
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
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
Sequence in context: A317682 A216651 A071338 * A051950 A341062 A172353
KEYWORD
nonn,base
AUTHOR
Reinhard Zumkeller, Dec 08 2002
STATUS
approved

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Last modified July 13 02:50 EDT 2024. Contains 374265 sequences. (Running on oeis4.)