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 A078822 Number of distinct binary numbers contained as substrings in the binary representation of n. 30
 1, 1, 3, 2, 4, 4, 5, 3, 5, 5, 5, 6, 7, 7, 7, 4, 6, 6, 6, 7, 7, 6, 8, 8, 9, 9, 9, 9, 10, 10, 9, 5, 7, 7, 7, 8, 7, 8, 9, 9, 9, 9, 7, 9, 11, 10, 11, 10, 11, 11, 11, 11, 12, 11, 11, 12, 13, 13, 13, 13, 13, 13, 11, 6, 8, 8, 8, 9, 8, 9, 10, 10, 9, 8, 10, 11, 11, 12, 12, 11, 11, 11, 11, 12, 10, 8 (list; graph; refs; listen; history; text; internal format)
 OFFSET 0,3 COMMENTS For n>0: 00: a(2^k-2) = 2*(k-1)+1, a(2^k-1) = k, a(2^k) = k+2; for k>1: a(2^k+1) = k+2; for k>0: a(2^k-1) = A078824(2^k-1), a(2^k) = A078824(2^k). EXAMPLE n=10 -> '1010' contains 5 different binary numbers: '0' (b0bb or bbb0), '1' (1bbb or bb1b), '10' (10bb or bb10), '101' (101b) and '1010' itself, therefore a(10)=5. MAPLE a:= n-> (s-> nops({seq(seq(parse(s[i..j]), i=1..j), j=1..length(s))}))(""||(convert(n, binary))): seq(a(n), n=0..85); # Alois P. Heinz, Jan 20 2021 MATHEMATICA a[n_] := (id = IntegerDigits[n, 2]; nd = Length[id]; Length[ Union[ Flatten[ Table[ id[[j ;; k]], {j, 1, nd}, {k, j, nd}], 1] //. {0, b__} :> {b}]]); Table[ a[n], {n, 0, 85}] (* Jean-François Alcover, Dec 01 2011 *) PROG (Haskell) a078822 = length . a119709_row import Numeric (showIntAtBase) -- Reinhard Zumkeller, Aug 13 2013, Sep 14 2011 (PARI) a(n) = {if (n==0, 1, vb = binary(n); vf = []; for (i=1, #vb, for (j=1, #vb - i + 1, pvb = vector(j, k, vb[i+k-1]); f = subst(Pol(pvb), x, 2); vf = Set(concat(vf, f)); ); ); #vf); } \\ Michel Marcus, May 08 2016; corrected Jun 13 2022 (Python) def a(n): return 1 if n == 0 else len(set(((((2<>i for i in range(n.bit_length()) for l in range(n.bit_length()-i))) print([a(n) for n in range(64)]) # Michael S. Branicky, Jul 28 2022 CROSSREFS Cf. A078823, A078826, A078824, A007088, A141297, A144623, A144624. Sequence in context: A322348 A321232 A326015 * A224980 A154392 A069745 Adjacent sequences: A078819 A078820 A078821 * A078823 A078824 A078825 KEYWORD nonn,base,nice,look AUTHOR Reinhard Zumkeller, Dec 08 2002 STATUS approved

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Last modified June 9 08:19 EDT 2023. Contains 363168 sequences. (Running on oeis4.)