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A266204 a(n) = G_n(5), where G_n(k) is the Goodstein function defined in A266201. 23
5, 27, 255, 467, 775, 1197, 1751, 2454, 3325, 4382, 5643, 7126, 8849, 10830, 13087, 15637, 18499, 21691, 25231, 29137, 33427, 38119, 43231, 48781, 54787, 61267, 68239, 75721, 83731, 92287, 101407, 111108, 121409, 132328, 143883, 156092, 168973, 182544, 196823 (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_0(5) = 5;

G_1(5) = B_2(5) - 1 = B_2(2^2 + 1) - 1 = 27;

G_2(5) = B_3(3^3) - 1 = 4^4 - 1 = 255;

G_3(5) = B_4(3*4^3 + 3*4^2 + 3*4 + 3) - 1 = 3*5^3 + 3*5^2 + 3*5 + 3 - 1 = 467.

PROG

(PARI) bump(a, n) = {if (a < n, return (a)); my(pd = Pol(digits(a, n)));  my(de = vector(poldegree(pd)+1, k, k--; polcoeff(pd, k))); my(bde = vector(#de, k, k--; bump(k, n))); my(q = sum(k=0, poldegree(pd), if (c=polcoeff(pd, k), c*x^bde[k+1], 0))); return(subst(q, x, n+1)); }

lista(nn) = {print1(a = 5, ", "); for (n=2, nn, a = bump(a, n)-1; print1(a, ", "); ); } \\ Michel Marcus, Feb 28 2016

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), A059936: G_5(n), A266201: G_n(n).

Sequence in context: A167019 A230563 A204266 * A300621 A265907 A135627

Adjacent sequences:  A266201 A266202 A266203 * A266205 A266206 A266207

KEYWORD

nonn,fini

AUTHOR

Natan Arie Consigli, Jan 22 2016

STATUS

approved

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Last modified January 29 08:12 EST 2020. Contains 331337 sequences. (Running on oeis4.)