The OEIS mourns the passing of Jim Simons and is grateful to the Simons Foundation for its support of research in many branches of science, including the OEIS.
login
The OEIS is supported by the many generous donors to the OEIS Foundation.

 

Logo
Hints
(Greetings from The On-Line Encyclopedia of Integer Sequences!)
A275749 Prime numbers of the form 2*4^n - 27. 4
5, 101, 524261, 8388581 (list; graph; refs; listen; history; text; internal format)
OFFSET
1,1
COMMENTS
Values of the exponent n are given in A275767, and every exponent (except for the first one) is odd. Consequently, after a(1) = 5, the rightmost digit of each term in this sequence will be 1.
As seen in the link below, a(5) = 2*4^291 - 27 > 3.1658 * 10^175. As a result of the recent extensions to A275767 by Vincenzo Librandi,
a(6) = 2*4^1263 - 27 > 5.0442 * 10^760
a(7) = 2*4^2661 - 27 > 2.4136 * 10^1602
a(8) = 2*4^3165 - 27 > 6.6206 * 10^1905
a(9) > 2*4^5000 - 27 > 3.9901 * 10^3010.
These primes a(m) can be used to generate numbers having abundance 26. The formula a(m)*(a(m)+27)/2 produces some of the terms in A275701.
LINKS
FORMULA
a(m) = 2*4^A275767(m) - 27.
EXAMPLE
a(1) = 2*4^A275767(1) - 27 = 2*4^2 - 27 = 32 - 27 = 5.
a(2) = 2*4^A275767(2) - 27 = 2*4^3 - 27 = 128 - 27 = 101.
a(3) = 2*4^A275767(3) - 27 = 2*4^9 - 27 = 524288 - 27 = 524261.
a(4) = 2*4^A275767(4) - 27 = 2*4^11 - 27 = 8388608 - 27 = 8388581.
MATHEMATICA
Select[2*4^Range[2, 200] - 27, PrimeQ] (* Michael De Vlieger, Aug 08 2016 *)
CROSSREFS
Sequence in context: A349045 A337831 A337828 * A057207 A124986 A231830
KEYWORD
nonn,more
AUTHOR
Timothy L. Tiffin, Aug 07 2016
STATUS
approved

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

License Agreements, Terms of Use, Privacy Policy. .

Last modified May 29 18:36 EDT 2024. Contains 372952 sequences. (Running on oeis4.)