A271554 a(n) = G_n(7), where G is the Goodstein function defined in A266201.

7, 30, 259, 3127, 46657, 823543, 16777215, 37665879, 77777775, 150051213, 273624711, 475842915, 794655639, 1281445305, 2004318063, 3051893870, 4537630813, 6604718946, 9431578931, 13238000758, 18291957825, 24917131658, 33501182551, 44504801406, 58471578053, 76038721330

Offset: 0

Author

Natan Arie Consigli, Apr 10 2016

Keywords

• nonn
• fini

Examples

			G_1(7) = B_2(7) - 1 = B[2](2^2 + 2 + 1) - 1 = 3^3 + 3 + 1 - 1 = 30;
G_2(7) = B_3(G_1(7)) - 1 = B[3](3^3 + 3) - 1 =  4^4 + 4 - 1 = 259;
G_3(7) = B_4(G_2(7)) - 1 = 5^5 + 3 - 1 = 3127;
G_4(7) = B_5(G_3(7)) - 1 = 6^6 + 2 - 1 = 46657;
G_5(7) = B_6(G_4(7)) - 1 = 7^7 + 1 - 1 = 823543;
G_6(7) = B_7(G_5(7)) - 1 = 8^8 - 1 = 16777215;
G_7(7) = B_8(G_6(7)) - 1 = 7*9^7 + 7*9^6 + 7*9^5 + 7*9^4 + 7*9^3 + 7*9^2 + 7*9 + 7 - 1 = 37665879.
		

Links

• Nicholas Matteo, Table of n, a(n) for n = 0..10000
• R. L. Goodstein, On the Restricted Ordinal Theorem, The Journal of Symbolic Logic 9, no. 2 (1944), 33-41.
• Wikipedia, Goodstein sequence

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), A266201: G_n(n).

Programs

PARI

lista(nn) = {print1(a = 7, ", "); 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, ", "); ); }