login
This site is supported by donations to The OEIS Foundation.

 

Logo

Annual Appeal: Please make a donation (tax deductible in USA) to keep the OEIS running. Over 5000 articles have referenced us, often saying "we discovered this result with the help of the OEIS".

Hints
(Greetings from The On-Line Encyclopedia of Integer Sequences!)
A082101 Primes of form 2^k + 3^k. 35
2, 5, 13, 97 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,1

COMMENTS

Next term, if it exists, is > 10^125074. - David Wasserman, Aug 13 2004

Since x+y is a factor of x^m+y^m if m is odd, 2^m+3^m is divisible by 2+3=5 unless m is zero or a power of 2. This is similar to Fermat numbers 1+2^m. - Michael Somos, Aug 27 2004

Checked k being powers of two through 2^21. Thus a(5) > 10^2000000. Primes of this magnitude are rare (about 1 in 4.6 million), so chance of finding one is remote with today's computer algorithms and speeds. - Robert Price, Apr 25 2013

If a(5) exists it is greater than 10^16000000. Probably finite and full. - Charles R Greathouse IV, Apr 29 2013

LINKS

Table of n, a(n) for n=1..4.

EXAMPLE

m=0: 1+1, m=1: 2+3, m=2: 4+9, m=4: 16+81.

MATHEMATICA

a={}; Do[If[PrimeQ[p=2^n+3^n], AppendTo[a, p]], {n, 0, 10^3}]; a (* Vladimir Joseph Stephan Orlovsky, Aug 07 2008 *)

Select[Table[2^k+3^k, {k, 0, 100}], PrimeQ] (* Harvey P. Dale, May 14 2014 *)

PROG

(PARI) print1(2); for(n=0, 99, if(ispseudoprime(t=2^(2^n)+3^(2^n)), print1(", "t))) \\ Charles R Greathouse IV, Jul 19 2011

CROSSREFS

Cf. A094474-A094499.

Sequence in context: A075742 A075737 A100843 * A158712 A090472 A120266

Adjacent sequences:  A082098 A082099 A082100 * A082102 A082103 A082104

KEYWORD

nonn

AUTHOR

Labos Elemer, Apr 14 2003

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 | More pages
The OEIS Community | Maintained by The OEIS Foundation Inc.

License Agreements, Terms of Use, Privacy Policy .

Last modified December 10 23:07 EST 2016. Contains 279021 sequences.