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A078826
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Number of distinct primes contained as binary substrings in binary representation of n.
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13
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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
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OFFSET
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0,6
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COMMENTS
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LINKS
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EXAMPLE
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n=7 -> '111' contains 2 different binary substrings which are primes: '11' (11b or b11) and '111' itself, therefore a(7)=2.
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MATHEMATICA
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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 *)
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PROG
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(Haskell)
a078826 n | n <= 1 = 0
| otherwise = length $ a225243_row n
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CROSSREFS
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KEYWORD
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nonn,base
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AUTHOR
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STATUS
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approved
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