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!)
A287218 a(n) = smallest k such that (6*k-3)*2^prime(n) - 1 is prime. 1
1, 1, 3, 1, 1, 2, 3, 9, 12, 8, 3, 4, 3, 1, 36, 25, 8, 12, 19, 21, 3, 12, 19, 40, 9, 14, 1, 14, 2, 18, 81, 56, 49, 38, 38, 26, 3, 33, 103, 12, 67, 12, 11, 8, 48, 79, 2, 43, 136, 82, 12, 46, 78, 31, 117, 126, 34, 4, 27, 49, 83, 3, 57, 234, 12, 10, 116, 128, 53, 13 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,3

COMMENTS

For n from 1 to 2000, a(n)/prime(n) is always < 1.8.

As N increases, (Sum_{n=1..N} a(n)) / (Sum_{n=1..N} prime(n)) tends to log(2)/3; this is consistent with the prime number theorem as the probability that x*2^n-1 is prime with odd x divisible by 3 is ~ 3/(n*log(2)) and after n*log(2)/3 try (n*log(2)/3)*(3/(n*log(2)) = 1.

LINKS

Pierre CAMI, Table of n, a(n) for n = 1..2000

FORMULA

a(n) = A285808(A000040(n)).

MATHEMATICA

sk[n_]:=Module[{k=1, t=2^Prime[n]}, While[!PrimeQ[(6k-3)*t-1], k++]; k]; Array[ sk, 70] (* Harvey P. Dale, Nov 14 2018 *)

CROSSREFS

Subsequence of A285808.

Cf. A284325, A284631.

Sequence in context: A128316 A065836 A078712 * A306438 A221978 A035254

Adjacent sequences:  A287215 A287216 A287217 * A287219 A287220 A287221

KEYWORD

nonn

AUTHOR

Pierre CAMI, May 22 2017

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 November 30 11:07 EST 2021. Contains 349419 sequences. (Running on oeis4.)