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A271556
a(n) = G_n(9), where G is the Goodstein function defined in A266201.
11
9, 81, 1023, 9842, 140743, 2471826, 50333399, 1162263921, 30000003325, 855935016215, 26748301350411, 908625319783885, 33336020476682897, 1313681671142588955, 55340232221128667935, 2481720785659010308168, 118039224225889612744771, 5935258966980940767393628
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(9) = B_2(9)-1 = B_2(2^(2+1)+1)-1 = 3^(3+1) + 1-1 = 81;
G_2(9) = B_3(3^(3+1))-1 = 4^(4+1)-1 = 1023;
G_3(9) = B_4(3*4^4 + 3*4^3 + 3*4^2 + 3*4 + 3)-1 = 3*5^5 + 3*5^3 + 3*5^2 + 3*5 + 3-1 = 9842;
G_4(9) = B_5(3*5^5 + 3*5^3 + 3*5^2 + 3*5 + 2)-1 = 3*6^6 + 3*6^3 + 3*6^2 + 3*6 + 2-1 = 140743;
G_5(9) = B_6(3*6^6 + 3*6^3 + 3*6^2 + 3*6 + 1)-1 = 3*7^7 + 3*7^3 + 3*7^2 + 3*7 + 1-1 = 2471826;
G_6(9) = B_7(3*7^7 + 3*7^3 + 3*7^2 + 3*7)-1 = 3*8^8 + 3*8^3 + 3*8^2 + 3*8-1 = 50333399.
PROG
(PARI) lista(nn) = {print1(a = 9, ", "); 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), A271554: G_n(7), A271555: G_n(8), A266201: G_n(n).
Sequence in context: A104266 A061433 A069659 * A368446 A110853 A371640
KEYWORD
nonn,fini
AUTHOR
Natan Arie Consigli, Apr 10 2016
STATUS
approved