A271561 - OEIS

%I #11 Jan 11 2020 15:57:47

%S 14,110,1281,18750,326591,5862840,134404971,3487116548,100000555551,

%T 3138429262496,106993206736331,3937376387710451,155568095560708189,

%U 6568408355716958693,295147905179358418247,14063084452067732533983,708235345355337686361209,37589973457545958206423881

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

%H Nicholas Matteo, <a href="/A271561/b271561.txt">Table of n, a(n) for n = 0..383</a>

%e G_1(14) = B_2(14)-1 = B_2(2^(2+1)+2^2+2)-1 = 3^(3+1)+3^3+3-1 = 110;

%e G_2(14) = B_3(3^(3+1)+3^3+2)-1 = 4^(4+1)+4^4+2-1 = 1281;

%e G_3(14) = B_4(4^(4+1)+4^4+1)-1 = 5^(5+1)+5^5+1-1 = 18750;

%e G_4(14) = B_5(5^(5+1)+5^5)-1 = 6^(6+1)+6^6-1 = 326591.

%o (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, ", "); ); }

%Y 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).

%K nonn,fini

%O 0,1

%A _Natan Arie Consigli_, Apr 13 2016