cp's OEIS Frontend

A348842 Number of Juniper Green games with n cards.

%I A348842 #10 Apr 09 2022 13:23:12
%S A348842 0,1,1,6,10,35,47,147,216,452,512,3055,3365,5602,12160,35951,37959,
%T A348842 147889,154998,703094,1178850,1467813
%N A348842 Number of Juniper Green games with n cards.
%C A348842 For the rules of this two person game with cards labeled from 1 to n, for n >= 1, called JG(n), see the Ian Stewart links.
%C A348842 It is reported (see the FEEDBACK and the German version), that E. P. Wigner used this game in some lecture in the thirties. There the prime factorization of n! into prime powers, with the number of odd or even (>= 2) exponents, seems to have played a role (see A055460(n) and A348841(n) for the number of primes with these exponents in the factorization of n!, respectively).
%C A348842 The repertoire of card numbers for JG(n) that can be chosen if the latest removed card had label k is shown in A348390. Of course, only those card numbers not yet removed in earlier moves qualify. E.g., n = 4, k = 2: repertoire 1, 4.
%C A348842 The total number of games JG(n), for n >= 2, if the first removed card has label K = 2*k, for k = 1, 2, ... ,floor(n/2), is given in A348843.
%C A348842 For the irregular table which gives in row n the odd and even number of moves in the a(n) JG(n) games see A348844. This gives the number of times Alice (the first mover), respectively Bob wins.
%H A348842 Ian Stewart, <a href="https://www.jstor.org/stable/24993666">Juniper Green</a>, Scientific American No. 3 March 1997, pp. 118-120.
%H A348842 Ian Stewart, <a href="https://www.jstor.org/stable/24996011">FEEDBACK</a>, Scientific American No. 5 November 1997 p. 112.
%H A348842 The author's email is given, <a href="http://playjunipergreen.com">juniper green</a> Online game with 100 cards.
%F A348842 a(n) = Sum_{k=1..floor(n/2)} A348843(n, k) = Sum_{k=1..2*floor(n/2)} A348844(n, k), for n >= 2.
%Y A348842 Cf. A055460, A348390, A348843, A348844.
%K A348842 nonn,more
%O A348842 1,4
%A A348842 _Wolfdieter Lang_, Dec 23 2021