|
|
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
|
|
|
FORMULA
|
|
|
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
|
|
|
KEYWORD
|
nonn
|
|
AUTHOR
|
|
|
STATUS
|
approved
|
|
|
|