proposed

reviewed

editing

proposed

11, 84, 1027, 15627, 279937, 5764801, 134217727, 2749609302, 70077777775, 1997331745489, 62412976762502, 2120126221988685, 77784048573561750, 30652572339474609291997331745490, 62412976762503, 2120126221988686, 77784048573561751, 3065257233947460930

Terms a(9)-a(13) corrected by Nicholas Matteo, Aug 15 2019

approved

editing

reviewed

approved

proposed

reviewed

editing

proposed

11, 84, 1027, 15627, 279937, 5764801, 134217727, 2749609302, 70077777775, 1997331745489, 62412976762502, 2120126221988685, 77784048573561750, 3065257233947460929

(PARI) lista(nn) = {print1(a = 10, 11, ", "); 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, ", "); ); }

nonn,new,fini

approved

editing

proposed

approved

editing

proposed

allocated for Natan Arie' Consigli

a(n) = G_n(11), where G is the Goodstein function defined in A266201.

84, 1027, 15627, 279937, 5764801, 134217727, 2749609302, 70077777775, 1997331745489, 62412976762502, 2120126221988685, 77784048573561750, 3065257233947460929

0,1

G_1(11) = B_2(11)-1 = B_2(2^(2+1)+2+1)-1 = 3^(3+1)+3+1-1 = 84;

G_2(11) = B_3(3^(3+1)+3)-1 = 4^(4+1)+4-1 = 1027;

G_3(11) = B_4(4^(4+1)+3)-1 = 5^(5+1)+3-1 = 15627;

G_4(11) = B_5(5^(5+1)+2)-1 = 6^(6+1)+2-1 = 279937;

G_5(11) = B_6(6^(6+1)+1)-1 = 7^(7+1)+1-1 = 5764801;

G_6(11) = B_7(7^(7+1))-1 = 8^(8+1)-1 = 134217727.

(PARI) lista(nn) = {print1(a = 10, ", "); 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, ", "); ); }

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), A266201: G_n(n).

allocated

nonn

Natan Arie' Consigli, Apr 11 2016

approved

editing