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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 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 October 15 04:45 EDT 2018. Contains 316200 sequences. (Running on oeis4.)