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 A145653 a(n) = the length of the longest substring of digits that occurs both in the binary representation of the n-th prime and in the binary representation of the (n+1)th prime. 1
 1, 1, 1, 2, 3, 2, 3, 3, 3, 3, 1, 4, 4, 4, 3, 4, 5, 2, 5, 3, 4, 5, 4, 4, 4, 5, 3, 4, 3, 3, 2, 4, 6, 5, 6, 4, 4, 5, 4, 5, 5, 4, 2, 5, 6, 4, 4, 3, 5, 4, 5, 4, 5, 2, 6, 6, 7, 4, 5, 7, 3, 4, 6, 5, 6, 4, 5, 5, 6, 4, 6, 5, 5, 5, 6, 3, 5, 5, 5, 4, 6, 5, 4, 6, 6, 4, 5, 6, 7, 5, 5, 4, 5, 5, 6, 7, 2, 8, 5, 5, 6, 5, 6, 8, 4 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,4 LINKS Harvey P. Dale, Table of n, a(n) for n = 1..1000 EXAMPLE The 12th prime is 37, which is 100101 in binary. The 13th prime is 41, which is 101001 in binary. The largest string of digits occurring in both binary representations is 1001, which occurs like so: (1001)01 and 10(1001). a(12) therefore equals 4 because 1001 contains 4 digits. MATHEMATICA lsub[n_]:=Module[{p1=IntegerDigits[Prime[n], 2], p2=IntegerDigits[ Prime[ n+1], 2]}, Flatten[ Table[ Partition[p1, k, 1], {k, Length[p1]}], 1]]; Table[ Max[ Length/@Intersection[lsub[x], lsub[x+1]]], {x, 120}] (* Harvey P. Dale, Dec 09 2017 *) CROSSREFS Sequence in context: A164886 A091935 A086063 * A266119 A026263 A080098 Adjacent sequences:  A145650 A145651 A145652 * A145654 A145655 A145656 KEYWORD base,nonn AUTHOR Leroy Quet, Oct 15 2008 EXTENSIONS Extended by Ray Chandler, Oct 27 2008 STATUS approved

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Last modified June 19 19:11 EDT 2019. Contains 324222 sequences. (Running on oeis4.)