1,2

Every entry is an odd number. a(n) <= a(n+1) <= a(n)+4. For all large enough n we know Cn/log(n) < a(n) < Kn/log(n) for suitable constants 0<C<K. Additional entries should be within the reach of computers. a(19) >= 5.

P. Erdos and L. Moser: On the representation of directed graphs as unions of orderings, Publ. Math. Inst. Hungar. Acad. Sci. 9 (1964) 125-132; also reprinted in Paul Erdos: The art of counting, Selected writings (ed. Joel Spencer) MIT Press 1973, pp. 79-86.

Richard Stearns: The voting problem, Amer. Math. Monthly 66 (1959) 761-763. Warning: Erdos, Moser and Stearns actually consider a slightly different problem definition, where ties are allowed. That would define a different sequence which would upper-bound this one and is related to it, but the present sequence seems to be a little more pleasant.

Warren D. Smith, Answer to puzzle 28 (surveys the problem)

Sequence in context: A082127 A031354 A033700 this_sequence A132973 A107760 A138070

Adjacent sequences: A122913 A122914 A122915 this_sequence A122917 A122918 A122919

hard,more,nonn

Warren D. Smith (warren.wds(AT)gmail.com), Sep 19 2006