OFFSET
1,2
COMMENTS
Size of prime gap containing the number 5^n, for n > 1.
From Gauss's prime counting function approximation, the expected gap size should be approximately n*log(5), however, the observed values seem to be closer to n*log(25) = n*A016648.
The arithmetic mean of a(n)/n for the terms 2..500 is 3.220 ~ 2*log(5) = A016648.
LINKS
A.H.M. Smeets, Table of n, a(n) for n = 1..500
A.H.M. Smeets, Values of a(n)/n for n=2..500 ordered versus (n-1)/499
MATHEMATICA
a[1] = 0; a[n_] := First @ Differences @ NextPrime[5^n, {-1, 1}]; Array[a, 60] (* Amiram Eldar, Oct 30 2020 *)
PROG
(PARI) a(n) = if (n==1, 0, my(pw=5^n); nextprime(pw+1) - precprime(pw-1)); \\ Michel Marcus, Oct 27 2020
CROSSREFS
KEYWORD
nonn
AUTHOR
A.H.M. Smeets, Oct 25 2020
STATUS
approved