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 A342263 a(n) is the length of the longest substring appearing twice (possibly with overlap) in the binary expansion of n. 2
 0, 0, 0, 1, 1, 1, 1, 2, 2, 1, 2, 1, 1, 1, 2, 3, 3, 2, 2, 1, 2, 3, 2, 2, 2, 1, 2, 2, 2, 2, 3, 4, 4, 3, 2, 2, 3, 2, 2, 2, 2, 2, 4, 3, 2, 3, 2, 3, 3, 2, 2, 2, 2, 3, 3, 2, 2, 2, 2, 2, 3, 3, 4, 5, 5, 4, 3, 3, 3, 2, 2, 2, 3, 4, 3, 2, 3, 2, 2, 3, 3, 2, 3, 2, 4, 5, 3 (list; graph; refs; listen; history; text; internal format)
 OFFSET 0,8 COMMENTS We ignore leading zeros, but the duplicate substrings can have leading zeros. This sequence diverges (for any k > 0, a number n with k*(2^k+1) or more binary digits has necessarily a length-k repeated substring in its binary expansion, so a(n) >= k). LINKS Rémy Sigrist, Table of n, a(n) for n = 0..8192 FORMULA a(n) < A070939(n). a(2^k) = a(2^k-1) = k-1 for any k > 0. EXAMPLE The first terms, alongside the binary expansion of n and the corresponding longest repeated substrings, are:   n   a(n)  bin(n)  longest duplicate substrings   --  ----  ------  ----------------------------    0     0       0  ""    1     0       1  ""    2     0      10  ""    3     1      11  "1"    4     1     100  "0"    5     1     101  "1"    6     1     110  "1"    7     2     111  "11"    8     2    1000  "00"    9     1    1001  "0", "1"   10     2    1010  "10"   11     1    1011  "1"   12     1    1100  "0", "1"   13     1    1101  "1"   14     2    1110  "11"   15     3    1111  "111" PROG (PARI) a(n) = { my (b=if (n, binary(n), [0])); for (w=1, oo, my (s=vector(#b+1-w, o, b[o..o+w-1])); if (#s==#Set(s), return (w-1))) } (Python) def a(n):   b = bin(n)[2:]   for k in range(len(b), -1, -1):     for i in range(len(b)-k):       for j in range(i+1, len(b)-k+1):         if b[i:i+k] == b[j:j+k]: return k print([a(n) for n in range(87)]) # Michael S. Branicky, Mar 07 2021 CROSSREFS Cf. A070939, A342298. Sequence in context: A218450 A025912 A029441 * A109495 A164295 A035214 Adjacent sequences:  A342260 A342261 A342262 * A342264 A342265 A342266 KEYWORD nonn,base AUTHOR Rémy Sigrist, Mar 07 2021 STATUS approved

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Last modified September 27 08:39 EDT 2021. Contains 347689 sequences. (Running on oeis4.)