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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 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

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