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

 

Logo


Hints
(Greetings from The On-Line Encyclopedia of Integer Sequences!)
A094473 Smallest prime factor of 2^n+3^n. 21
5, 13, 5, 97, 5, 13, 5, 17, 5, 13, 5, 97, 5, 13, 5, 3041, 5, 13, 5, 41, 5, 13, 5, 17, 5, 13, 5, 97, 5, 13, 5, 1153, 5, 13, 5, 97, 5, 13, 5, 17, 5, 13, 5, 89, 5, 13, 5, 193, 5, 13, 5, 97, 5, 13, 5, 17, 5, 13, 5, 41, 5, 13, 5, 769, 5, 13, 5, 97, 5, 13, 5, 17, 5, 13, 5 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,1

LINKS

Antti Karttunen, Table of n, a(n) for n = 1..1023

FORMULA

a(n) = A020639(A007689(n)). - Antti Karttunen, Nov 01 2018

EXAMPLE

If n=4k+1 or 4k+3 then 2^n+3^n is divisible by 5.

If n=4k+2 then 2^n+3^n is divisible by 13.

Case n=4k including especially n=2^j cannot be discussed with elementary tools and primality of 2^n+3^n remains open.

MATHEMATICA

mif[x_]:=Part[Flatten[FactorInteger[x]], 1] Table[mif[2^w+3^w], {w, 1, 75}]

FactorInteger[#][[1, 1]]&/@Table[2^n+3^n, {n, 80}] (* Harvey P. Dale, Mar 26 2019 *)

PROG

(PARI) a(n)=factor(2^n+3^n)[1, 1] \\ Charles R Greathouse IV, Apr 29 2015

(PARI) A094473(n) = { my(k=(2^n+3^n)); forprime(p=2, k, if(!(k%p), return(p))); }; \\ Antti Karttunen, Nov 01 2018

(GAP) List([1..80], n->Factors(2^n+3^n)[1]); # Muniru A Asiru, Nov 01 2018

CROSSREFS

Cf. A007689, A020639, A082101, A094474-A094494.

Sequence in context: A170864 A293958 A089619 * A068530 A088315 A138296

Adjacent sequences:  A094470 A094471 A094472 * A094474 A094475 A094476

KEYWORD

nonn

AUTHOR

Labos Elemer, Jun 02 2004

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 May 19 04:06 EDT 2019. Contains 323377 sequences. (Running on oeis4.)