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 A338376 (Smallest prime >= 6^n) - (largest prime <= 6^n). 3
 2, 6, 12, 6, 30, 14, 22, 18, 32, 12, 94, 54, 52, 18, 98, 66, 84, 18, 36, 18, 30, 138, 80, 96, 30, 142, 36, 80, 52, 26, 78, 64, 126, 138, 94, 136, 162, 276, 110, 162, 206, 94, 78, 324, 186, 128, 118, 56, 102, 390, 78, 90, 18, 62, 94, 108, 220, 100, 336, 618 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,1 COMMENTS Size of prime gap containing the number 6^n, for n > 1. From Gauss's prime counting function approximation, the expected gap size should be approximately n*log(6), however, the observed values seem to be closer to n*log(36) = n*A016659. The arithmetic mean of a(n)/n for the terms 1..1000 is 3.605 ~ 2*log(6). LINKS A.H.M. Smeets, Table of n, a(n) for n = 1..1000 FORMULA a(n) = A013607(n) + A013600(n). MATHEMATICA a[n_] := First @ Differences @ NextPrime[6^n, {-1, 1}]; Array[a, 60] (* Amiram Eldar, Oct 30 2020 *) PROG (PARI) a(n) = my(pw=6^n); nextprime(pw+1) - precprime(pw-1); \\ Michel Marcus, Oct 27 2020 CROSSREFS Cf. A013600, A013607, A016659. Cf. A058249 (2^n), A338155 (3^n), A338419 (5^n), A038804 (10^n). Sequence in context: A165822 A014965 A074259 * A113540 A111658 A341664 Adjacent sequences:  A338373 A338374 A338375 * A338377 A338378 A338379 KEYWORD nonn AUTHOR A.H.M. Smeets, Oct 26 2020 STATUS approved

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Last modified December 7 20:19 EST 2021. Contains 349588 sequences. (Running on oeis4.)