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!)
A159625 Numbers n such that 2^x + 3^y is never prime when max(x,y) = n 3
1679, 1743, 4980, 4982, 5314, 5513, 5695, 6100, 6578, 7251, 7406, 7642, 8218, 8331, 9475, 9578, 9749, 10735 (list; graph; refs; listen; history; text; internal format)
OFFSET
1,1
COMMENTS
Mark Underwood found that for each nonnegative integer n < 1421 there is at least one prime of the form 2^m + 3^n or 2^n + 3^m with m not exceeding n.
This sequence consists of numbers for which there is no such prime.
David Broadhurst estimated that a fraction in excess of 1/800 of the natural numbers belongs to this sequence and found 17 instances with n < 10^4.
For each of the remaining 9983 nonnegative integers n < 10^4, a prime or probable prime of the form 2^x + 3^y was found with max(x,y) = n.
Each probable prime was subjected to a combination of strong Fermat and strong Lucas tests.
LINKS
Broadhurst's heuristic in the PrimeNumbers list. [Broken link]
Maximilian Hasler, Mike Oakes, Mark Underwood, David Broadhurst and others, Primes of the form (x+1)^p-x^p, digest of 22 messages in primenumbers Yahoo group, Apr 5 - May 7, 2009. [Cached copy]
Underwood's posting in the PrimeNumbers list
A list of 9983 primes or probable primes for the excluded cases with n < 10^4
EXAMPLE
a(3) = 4980, since there is no prime of the form 2^m + 3^4980 or 2^4980 + 3^m with m < 4981 and 4980 is the third number n such that 2^x + 3^y is never prime when max(x,y) = n.
CROSSREFS
Sequence in context: A252300 A339960 A252442 * A156425 A247853 A093787
KEYWORD
nonn,more,hard
AUTHOR
David Broadhurst, Apr 17 2009
EXTENSIONS
a(18) from Giovanni Resta, Apr 09 2014
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 July 16 12:01 EDT 2024. Contains 374348 sequences. (Running on oeis4.)