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A271554
a(n) = G_n(7), where G is the Goodstein function defined in A266201.
16
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
0,1
LINKS
R. L. Goodstein, On the Restricted Ordinal Theorem, The Journal of Symbolic Logic 9, no. 2 (1944), 33-41.
EXAMPLE
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.
PROG
(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, ", "); ); }
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).
Sequence in context: A180786 A343755 A026653 * A296013 A196338 A196315
KEYWORD
nonn,fini
AUTHOR
Natan Arie Consigli, Apr 10 2016
STATUS
approved