A145653 - OEIS

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, 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

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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 * A346153 A266119 A026263

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