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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 (list; graph; refs; listen; history; text; internal format)
OFFSET

2,1

COMMENTS

A038003(n) = binomial(2^(n+1)-2, 2^n-1)/(2^n).

a(n) <> 3 iff the base-3 representation of 2^n-1 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^n-1;

  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^n-1]/(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

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Last modified December 11 05:41 EST 2017. Contains 295868 sequences.