

A120275


Smallest prime factor of the odd Catalan number A038003(n).


6



5, 3, 3, 7, 3, 3, 7, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3
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OFFSET

2,1


COMMENTS

A038003(n) = binomial(2^(n+1)2, 2^n1)/(2^n).
a(n) <> 3 iff the base3 representation of 2^n1 has no 2's. Conjecture: this only occurs for n = 2, 5, 8. I verified it up to n = 10^4.  Robert Israel, Nov 18 2015


LINKS

Table of n, a(n) for n=2..86.


EXAMPLE

a(2) = 5 because A038003(2) = 5.
a(3) = 3 because A038003(3) = 429 = 3*11*13.


MAPLE

f:= proc(n) local m;
m:= 2^n1;
if has(convert(m, base, 3), 2) then return 3 fi;
min(numtheory:factorset(binomial(2*m, m)/(m+1)));
end proc:
seq(f(n), n=2..1000); # Robert Israel, Nov 18 2015


MATHEMATICA

f[n_] := Block[{p = 2, m = Binomial[2^(n+1)2, 2^n1]/(2^n)}, While[Mod[m, p] > 0, p = NextPrime@ p]; p]; Array[f, 27, 2] (* Robert G. Wilson v, Nov 14 2015 *)


CROSSREFS

Cf. A038003, A000108.
Sequence in context: A198923 A056597 A019624 * A021656 A244683 A263157
Adjacent sequences: A120272 A120273 A120274 * A120276 A120277 A120278


KEYWORD

nonn


AUTHOR

Alexander Adamchuk, Jul 04 2006


EXTENSIONS

a(16)a(28) from Robert G. Wilson v, Nov 14 2015
a(29)a(86) from Robert Israel, Nov 18 2015


STATUS

approved



