A266204 a(n) = G_n(5), where G_n(k) is the Goodstein function defined in A266201.

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

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: A342904 A230563 A204266 * A360770 A360726 A360712

Adjacent sequences: A266201 A266202 A266203 * A266205 A266206 A266207

Keyword

nonn,fini

Author

Natan Arie Consigli, Jan 22 2016

Status

approved