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%I #101 Nov 30 2020 08:58:49
%S 0,4,6,4,10,6,24,10,6,22,36,74,30,10,18,124,44,20,70,16,60,6,52,30,34,
%T 22,42,48,144,30,20,104,122,90,50,12,52,18,140,156,72,126,126,42,68,
%U 90,98,100,66,74,50,174,30,38,126,72,30,378,102,176,108,130
%N (Smallest prime >= 3^n) - (largest prime <= 3^n).
%C Size of prime gap containing the number 3^n, for n > 1.
%C From Gauss's prime counting function approximation, the expected gap size should be approximately n*log(3), however, the observed values seem to be closer to n*log(8.72) ~ n*log(3^2) = n*A016632.
%H A.H.M. Smeets, <a href="/A338155/b338155.txt">Table of n, a(n) for n = 1..1000</a>
%F a(n) = A013598(n) + A013604(n) for n > 1.
%t a[1] = 0; a[n_] := First @ Differences @ NextPrime[3^n, {-1, 1}]; Array[a, 60] (* _Amiram Eldar_, Oct 30 2020 *)
%o (PARI) a(n) = if (n==1, 0, nextprime(3^n) - precprime(3^n)); \\ _Michel Marcus_, Oct 25 2020
%Y Cf. A013598, A013604, A016632.
%Y Cf. A058249 (for 2^n), A338419 (for 5^n), A338376 (for 6^n), A038804 (for 10^n).
%K nonn
%O 1,2
%A _A.H.M. Smeets_, Oct 25 2020
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