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

 

Logo

Thanks to everyone who made a donation during our annual appeal!
To see the list of donors, or make a donation, see the OEIS Foundation home page.

Hints
(Greetings from The On-Line Encyclopedia of Integer Sequences!)
A152765 Smallest prime divisor of Catalan number A000108(n), with a(0) = a(1) = 1. 3
1, 1, 2, 5, 2, 2, 2, 3, 2, 2, 2, 2, 2, 2, 2, 3, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 7, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 3, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,3

COMMENTS

a(n) <> 2 iff n = 2^k - 1 (A000225). In fact for k>1, a(2^k-1): 5, 3, 3, 7, 3, 3, 7, 3, 3, 3, 3, 3, 3, ..., . (A120275) - Robert G. Wilson v, Nov 14 2015

LINKS

Antti Karttunen, Table of n, a(n) for n = 0..65537

FORMULA

a(n) = A020639(A000108(n)). - Michel Marcus, Nov 14 2015

MATHEMATICA

FactorInteger[#][[1, 1]]&/@CatalanNumber[Range[2, 80]] (* Harvey P. Dale, Oct 08 2014 *)

PROG

(PARI) a(n) = factor(binomial(2*n, n)/(n+1))[1, 1]; \\ Michel Marcus, Nov 14 2015

(PARI) A152765(n) = if(n<2, 1, my(c=binomial(2*n, n)/(n+1)); forprime(p=2, oo, if(!(c%p), return(p)))); \\ Antti Karttunen, Jan 12 2019

(MAGMA) [Minimum(PrimeDivisors(Catalan(n))): n in [2..100]]; // Vincenzo Librandi, Jan 04 2017

CROSSREFS

Cf. A000108, A000225, A120275, A120303, A139044, A152761, A152762, A152763.

Sequence in context: A124780 A108437 A226029 * A286664 A242242 A171937

Adjacent sequences:  A152762 A152763 A152764 * A152766 A152767 A152768

KEYWORD

nonn,changed

AUTHOR

Omar E. Pol, Dec 15 2008, Jan 03 2009

EXTENSIONS

Terms a(0) = a(1) = 1 prepended and more terms added by Antti Karttunen, Jan 12 2019

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 January 17 18:48 EST 2019. Contains 319251 sequences. (Running on oeis4.)