|
%I #21 Jan 11 2020 15:57:47
%S 11,84,1027,15627,279937,5764801,134217727,2749609302,70077777775,
%T 1997331745490,62412976762503,2120126221988686,77784048573561751,
%U 3065257233947460930,129127208517971179375,5790681833207409243109,275424856527080300658781,13848937589622201728586799
%N a(n) = G_n(11), where G is the Goodstein function defined in A266201.
%H Nicholas Matteo, <a href="/A271558/b271558.txt">Table of n, a(n) for n = 0..384</a>
%H R. L. Goodstein, <a href="http://www.jstor.org/stable/2268019">On the Restricted Ordinal Theorem</a>, The Journal of Symbolic Logic 9, no. 2 (1944), 33-41.
%e G_1(11) = B_2(11)-1 = B_2(2^(2+1)+2+1)-1 = 3^(3+1)+3+1-1 = 84;
%e G_2(11) = B_3(3^(3+1)+3)-1 = 4^(4+1)+4-1 = 1027;
%e G_3(11) = B_4(4^(4+1)+3)-1 = 5^(5+1)+3-1 = 15627;
%e G_4(11) = B_5(5^(5+1)+2)-1 = 6^(6+1)+2-1 = 279937;
%e G_5(11) = B_6(6^(6+1)+1)-1 = 7^(7+1)+1-1 = 5764801;
%e G_6(11) = B_7(7^(7+1))-1 = 8^(8+1)-1 = 134217727.
%o (PARI) lista(nn) = {print1(a = 11, ", "); for (n=2, nn, pd = Pol(digits(a, n)); q = sum(k=0, poldegree(pd), if (c=polcoeff(pd, k), c*x^subst(Pol(digits(k, n)), x, n+1), 0)); a = subst(q, x, n+1) - 1; print1(a, ", "); ); }
%Y Cf. A056193: G_n(4), A059933: G_n(16), A211378: G_n(19), A215409: G_n(3), A222117: G_n(15), A266204: G_n(5), A266205: G_n(6), A271554: G_n(7), A271555: G_n(8), A271556: G_n(9), A271557: G_n(10), A266201: G_n(n).
%K nonn,fini
%O 0,1
%A _Natan Arie Consigli_, Apr 11 2016
%E a(9)-a(13) corrected by _Nicholas Matteo_, Aug 15 2019
%E a(14) onwards from _Nicholas Matteo_, Aug 28 2019
|
