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 A130742 Reciprocal of the base-2 logarithm of the ratio between consecutive primes, rounded down. 0
 1, 1, 2, 1, 4, 2, 6, 3, 2, 10, 3, 6, 14, 7, 5, 6, 20, 7, 11, 24, 8, 14, 9, 8, 17, 35, 18, 37, 19, 5, 22, 15, 47, 9, 51, 17, 18, 28, 19, 20, 62, 12, 66, 33, 68, 11, 12, 38, 79, 40, 27, 83, 17, 29, 30, 30, 93, 31, 48, 97, 19, 14, 53, 108, 54, 16, 38, 23, 120, 60, 41, 31, 42, 43, 66, 44, 34 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,3 COMMENTS a(n) is the largest power to which the fraction prime(n+1)/prime(n) can be raised without yielding a result which is greater than 2. It has been proved that lim inf of this sequence is (positive) infinity; e.g., the ratio between subsequent primes tends to 1. LINKS FORMULA a(n) = floor(1 / log_2(prime(n+1) / prime(n))). EXAMPLE a(5) = 4 because the sixth prime, 13, divided by the fifth prime, 11, has base-two logarithm 0.241008... and this lies between 1/4 and 1/5. MATHEMATICA f[n_] := Floor[1/Log[2, Prime[n + 1]/Prime[n]]] PROG (PARI) a(n) = log(2)\log(prime(n+1) / prime(n)); \\ Michel Marcus, Apr 14 2021 CROSSREFS Cf. A000523, A000040, A074461. Sequence in context: A109170 A225368 A099311 * A130107 A107130 A194747 Adjacent sequences:  A130739 A130740 A130741 * A130743 A130744 A130745 KEYWORD easy,nonn AUTHOR Jack W Grahl, Jul 07 2007 EXTENSIONS Edited by Jon E. Schoenfield, Apr 13 2021 STATUS approved

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Last modified July 29 09:41 EDT 2021. Contains 346344 sequences. (Running on oeis4.)