A271558 a(n) = G_n(11), where G is the Goodstein function defined in A266201.

11, 84, 1027, 15627, 279937, 5764801, 134217727, 2749609302, 70077777775, 1997331745490, 62412976762503, 2120126221988686, 77784048573561751, 3065257233947460930, 129127208517971179375, 5790681833207409243109, 275424856527080300658781, 13848937589622201728586799

Offset: 0

Author

Natan Arie Consigli, Apr 11 2016

Keywords

• nonn
• fini

Examples

			G_1(11) = B_2(11)-1 = B_2(2^(2+1)+2+1)-1 = 3^(3+1)+3+1-1 = 84;
G_2(11) = B_3(3^(3+1)+3)-1 = 4^(4+1)+4-1 = 1027;
G_3(11) = B_4(4^(4+1)+3)-1 = 5^(5+1)+3-1 = 15627;
G_4(11) = B_5(5^(5+1)+2)-1 = 6^(6+1)+2-1 = 279937;
G_5(11) = B_6(6^(6+1)+1)-1 = 7^(7+1)+1-1 = 5764801;
G_6(11) = B_7(7^(7+1))-1 = 8^(8+1)-1 = 134217727.
		

Links

• Nicholas Matteo, Table of n, a(n) for n = 0..384
• R. L. Goodstein, On the Restricted Ordinal Theorem, The Journal of Symbolic Logic 9, no. 2 (1944), 33-41.

Crossrefs

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).

Programs

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, ", "); ); }

Extensions

a(9)-a(13) corrected by Nicholas Matteo, Aug 15 2019

a(14) onwards from Nicholas Matteo, Aug 28 2019