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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 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,1

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

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

Adjacent sequences:  A271551 A271552 A271553 * A271555 A271556 A271557

KEYWORD

nonn,fini

AUTHOR

Natan Arie Consigli, Apr 10 2016

STATUS

approved

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Last modified July 30 17:04 EDT 2021. Contains 346359 sequences. (Running on oeis4.)