A268687 a(n) = MAX(g_k(n)) where g_k(n) is the function defined in A266202.

0, 1, 2, 3, 11, 31, 191, 1023

Offset

0,3

Links

Table of n, a(n) for n=0..7.

Example

g_1(4) = b_2(4)-1 = b_2(2^2)-1 = 3^2-1 = 8;
g_2(4) = b_3(2*3+2)-1 = 2*4 + 2-1 = 9;
g_3(4) = b_4(2*4 + 1 ) -1 = 2*5 + 1-1 = 10;
g_4(4) = b_5(2*5) -1= 2*6 - 1 = 11;
g_5(4) = b_6(6+5)-1 = 7+5-1 = 11;
g_6(4) = b_7(7+4)-1 = 8+4-1 = 11;
g_7(4) = b_8(8+3)-1 = 9+3-1 = 11;
g_8(4) = b_9(9+2)-1 = 10+2-1 = 11;
g_9(4) = b_10(10+1)-1 = 11+1-1 = 11;
g_10(4) = b_11(11)-1 = 12-1 = 11;
g_11(4) = b_12(11)-1 = 11-1 = 10;
g_12(4) = b_13(10)-1 = 10-1 = 9;
g_13(4) = b_14(9)-1 = 9-1 = 8;
…
g_21(4) = 0;
So a(4)=11.

Prog

(PARI) g(n, k) = {if (n == 0, return (k)); wn = k; for (k=2, n+1, pd = Pol(digits(wn, k)); wn = subst(pd, x, k+1) - 1; ); wn; }
a(n) = {vg = []; ok = 1; ns = 0; while(ok, newg = g(ns, n); vg = concat(vg, newg); if (newg <= 0, ok = 0); ns++; ); vmax = vecmax(vg); vmax; } \\ Michel Marcus, Apr 04 2016; corrected Jun 13 2022

Crossrefs

Cf. A266203, A268688, A268689.

Sequence in context: A235625 A032357 A144056 * A062630 A300771 A296005

Adjacent sequences: A268684 A268685 A268686 * A268688 A268689 A268690

Keyword

nonn,more

Author

Natan Arie Consigli, Apr 02 2016

Extensions

a(6)-a(7) from Michel Marcus, Apr 04 2016

Status

approved