A271561 a(n) = G_n(14), where G is the Goodstein function defined in A266201.

14, 110, 1281, 18750, 326591, 5862840, 134404971, 3487116548, 100000555551, 3138429262496, 106993206736331, 3937376387710451, 155568095560708189, 6568408355716958693, 295147905179358418247, 14063084452067732533983, 708235345355337686361209, 37589973457545958206423881

Offset

0,1

Links

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

Example

G_1(14) = B_2(14)-1 = B_2(2^(2+1)+2^2+2)-1 = 3^(3+1)+3^3+3-1 = 110;
G_2(14) = B_3(3^(3+1)+3^3+2)-1 = 4^(4+1)+4^4+2-1 = 1281;
G_3(14) = B_4(4^(4+1)+4^4+1)-1 = 5^(5+1)+5^5+1-1 = 18750;
G_4(14) = B_5(5^(5+1)+5^5)-1 = 6^(6+1)+6^6-1 = 326591.

Prog

(PARI) lista(nn) = {print1(a = 14, ", "); 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), A271556: G_n(9), A271557: G_n(10), A271558: G_n(11), A271559: G_n(12), A271560: G_n(13), A266201: G_n(n).

Sequence in context: A074886 A294445 A036395 * A215868 A244693 A039630

Adjacent sequences: A271558 A271559 A271560 * A271562 A271563 A271564

Keyword

nonn,fini

Author

Natan Arie Consigli, Apr 13 2016

Status

approved