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%I #50 Nov 30 2020 08:58:57
%S 2,6,12,6,30,14,22,18,32,12,94,54,52,18,98,66,84,18,36,18,30,138,80,
%T 96,30,142,36,80,52,26,78,64,126,138,94,136,162,276,110,162,206,94,78,
%U 324,186,128,118,56,102,390,78,90,18,62,94,108,220,100,336,618
%N (Smallest prime >= 6^n) - (largest prime <= 6^n).
%C Size of prime gap containing the number 6^n, for n > 1.
%C 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.
%C The arithmetic mean of a(n)/n for the terms 1..1000 is 3.605 ~ 2*log(6).
%H A.H.M. Smeets, <a href="/A338376/b338376.txt">Table of n, a(n) for n = 1..1000</a>
%F a(n) = A013607(n) + A013600(n).
%t a[n_] := First @ Differences @ NextPrime[6^n, {-1, 1}]; Array[a, 60] (* _Amiram Eldar_, Oct 30 2020 *)
%o (PARI) a(n) = my(pw=6^n); nextprime(pw+1) - precprime(pw-1); \\ _Michel Marcus_, Oct 27 2020
%Y Cf. A013600, A013607, A016659.
%Y Cf. A058249 (2^n), A338155 (3^n), A338419 (5^n), A038804 (10^n).
%K nonn
%O 1,1
%A _A.H.M. Smeets_, Oct 26 2020
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