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 A241786 Smallest k such that the number of the first even exponents in prime power factorization of (2*k)! is n, or a(n)=0 if there is no such k. 1
 1, 6, 3, 5, 10, 24, 27, 169, 924, 3168, 720, 3208, 408, 35421, 50878, 73920, 18757, 204513, 134418, 295680, 427684, 2746710, 6867848, 14476645, 7278558, 3668406, 737564, 245340483, 1931850660, 1514239096, 3228582476, 1325085081, 16188866895, 33517640073 (list; graph; refs; listen; history; text; internal format)
 OFFSET 0,2 COMMENTS Conjecture: 1) All a(n)>0; 2) a(2*n+1)>a(2*n). Conjecture (2) is wrong because a(24) = 7278558 >= a(25) = 3668406. a(35) > 10^11; a(36) = 8036409193. - Hiroaki Yamanouchi, Sep 29 2014 REFERENCES P. Erdős, P. L. Graham, Old and new problems and results in combinatorial number theory, L'Enseignement Mathematique, Imprimerie Kunding, Geneva, 1980. LINKS Giovanni Resta, Table of n, a(n) for n = 0..44 (terms a(0)-a(34) and a(36) from Hiroaki Yamanouchi) D. Berend, Parity of exponents in the factorization of n!, J. Number Theory, 64 (1997), 13-19. EXAMPLE a(2)=3, since (2*3)!= 2^4*3^2*5, and here the number of the first even exponents is 2. PROG (PARI) nbev(n) = {f = factor(n); nbe = 0; i = 1; while ((i <= #f~) && ((f[i, 2] % 2) == 0), i++; nbe++); nbe; } a(n) = {k = 0; while(nbev((2*k)!) != n, k++); k; } \\ Michel Marcus, Apr 30 2014 CROSSREFS Cf. A240537, A240606, A240620. Sequence in context: A085653 A022462 A319894 * A019151 A143506 A248580 Adjacent sequences:  A241783 A241784 A241785 * A241787 A241788 A241789 KEYWORD nonn AUTHOR Vladimir Shevelev, Apr 28 2014 EXTENSIONS More terms from Peter J. C. Moses, May 06 2014 a(21)-a(33) from Hiroaki Yamanouchi, Sep 29 2014 STATUS approved

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Last modified June 22 14:14 EDT 2021. Contains 345380 sequences. (Running on oeis4.)