A271560 a(n) = G_n(13), where G is the Goodstein function defined in A266201.

13, 108, 1279, 16092, 280711, 5765998, 134219479, 3486786855, 100000003325, 3138428381103, 106993205384715, 3937376385706415, 155568095557821073, 6568408355712901455, 295147905179352838943, 14063084452067725006646, 708235345355337676376131, 37589973457545958193377292

Offset

0,1

Links

Nicholas Matteo, Table of n, a(n) for n = 0..383

Example

G_1(13) = B_2(13)-1 = B_2(2^(2+1)+2^2+1)-1 = 3^(3+1)+3^3+1-1 = 108;
G_2(13) = B_3(3^(3+1)+3^3)-1 = 4^(4+1)+4^4-1 = 1279;
G_3(13) = B_4(4^(4+1)+3*4^3+3*4^2+3*4+3)-1 = 5^(5+1)+3*5^3+3*5^2+3*5+3-1 = 16092;
G_4(13) = B_5(5^(5+1)+3*5^3+3*5^2+3*5+2)-1 = 6^(6+1)+3*6^3+3*6^2+3*6+2-1 = 280711;
G_5(13) = B_6(6^(6+1)+3*6^3+3*6^2+3*6+1)-1 = 7^(7+1)+3*7^3+3*7^2+3*7+1-1 = 5765998;
G_6(13) = B_7(7^(7+1)+3*7^3+3*7^2+3*7)-1 = 8^(8+1)+3*8^3+3*8^2+3*8-1 = 134219479;
G_7(13) = B_8(8^(8+1)+3*8^3+3*8^2+2*8+7)-1 = 9^(9+1)+3*9^3+3*9^2+2*9+7-1 = 3486786855.

Prog

(PARI) lista(nn) = {my(a=13); print1(a, ", "); for (n=2, nn, my(pd = Pol(digits(a, n)), q = sum(k=0, poldegree(pd), my(c=polcoeff(pd, k)); if (c, 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), A271556: G_n(9), A271557: G_n(10), A271558: G_n(11), A271559: G_n(12), A266201: G_n(n).

Sequence in context: A038385 A084901 A006239 * A142040 A002648 A055840

Adjacent sequences: A271557 A271558 A271559 * A271561 A271562 A271563

Keyword

nonn,fini

Author

Natan Arie Consigli, Apr 11 2016

Status

approved