login
The OEIS Foundation is supported by donations from users of the OEIS and by a grant from the Simons Foundation.

 

Logo

Year-end appeal: Please make a donation to the OEIS Foundation to support ongoing development and maintenance of the OEIS. We are now in our 56th year, we are closing in on 350,000 sequences, and we’ve crossed 9,700 citations (which often say “discovered thanks to the OEIS”).

Hints
(Greetings from The On-Line Encyclopedia of Integer Sequences!)
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

Lookup | Welcome | Wiki | Register | Music | Plot 2 | Demos | Index | Browse | More | WebCam
Contribute new seq. or comment | Format | Style Sheet | Transforms | Superseeker | Recent
The OEIS Community | Maintained by The OEIS Foundation Inc.

License Agreements, Terms of Use, Privacy Policy. .

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