A137411 -id:A137411 - cp's OEIS frontend

A271991 g_n(10) where g is the weak Goodstein function defined in A266202.

10, 29, 65, 125, 215, 284, 363, 452, 551, 660, 779, 907, 1045, 1193, 1351, 1519, 1697, 1885, 2083, 2291, 2509, 2737, 2975, 3222, 3479, 3746, 4023, 4310, 4607, 4914, 5231, 5558, 5895, 6242, 6599, 6966, 7343, 7730, 8127, 8534, 8951

Offset: 0

Natan Arie Consigli, May 22 2016

For more info see A266201-A266202.

Cf. A271557: G_n(10).

Weak Goodstein sequences: A137411: g_n(11); A265034: g_n(266); A267647: g_n(4); A267648: g_n(5); A271987: g_n(6); A271988: g_n(7); A271989: g_n(8); A271990: g_n(9); A266202: g_n(n); A266203: a(n)=k such that g_k(n)=0;

g[k_, n_] := If[k == 0, n, Total@ Flatten@ MapIndexed[#1 (k + 2)^(#2 - 1) &, Reverse@ IntegerDigits[#, k + 1]] &@ g[k - 1, n] - 1]; Table[g[n, 10], {n, 0, 40}]

A271992 g_n(16) where g is the weak Goodstein function defined in A266202.

Original entry on oeis.org

16, 80, 169, 310, 515, 795, 1163, 1631, 2211, 2915, 3755, 4742, 5889, 7208, 8711, 10410, 12317, 14444, 16803, 19406, 22265, 25392, 28799, 32472, 36447, 40736, 45351, 50304, 55607, 61272, 67311, 73736, 80559, 87792, 95447, 103536, 112071

Offset: 0

Natan Arie Consigli, May 24 2016

For more information see A266201 and A266202.

Cf. A271557: G_n(10).

Weak Goodstein sequences: A267647: g_n(4); A267648: g_n(5); A271987: g_n(6); A271988: g_n(7); A271989: g_n(8); A271990: g_n(9); A271991: g_n(10); A137411: g_n(11); A265034: g_n(266); A266202: g_n(n); A266203: a(n)=k such that g_k(n)=0.

g[k_, n_] :=
If[k == 0, n,
  Total@Flatten@
       MapIndexed[#1 (k + 2)^(#2 - 1) &,
        Reverse@IntegerDigits[#, k + 1]] &@g[k - 1, n] - 1]; Table[
g[n, 16], {n, 0, 36}]

cp's OEIS Frontend

A271991 g_n(10) where g is the weak Goodstein function defined in A266202.

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