A268687 - OEIS

%I #16 Jun 13 2022 12:37:12

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

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

%e g_1(4) = b_2(4)-1 = b_2(2^2)-1 = 3^2-1 = 8;

%e g_2(4) = b_3(2*3+2)-1 = 2*4 + 2-1 = 9;

%e g_3(4) = b_4(2*4 + 1 ) -1 = 2*5 + 1-1 = 10;

%e g_4(4) = b_5(2*5) -1= 2*6 - 1 = 11;

%e g_5(4) = b_6(6+5)-1 = 7+5-1 = 11;

%e g_6(4) = b_7(7+4)-1 = 8+4-1 = 11;

%e g_7(4) = b_8(8+3)-1 = 9+3-1 = 11;

%e g_8(4) = b_9(9+2)-1 = 10+2-1 = 11;

%e g_9(4) = b_10(10+1)-1 = 11+1-1 = 11;

%e g_10(4) = b_11(11)-1 = 12-1 = 11;

%e g_11(4) = b_12(11)-1 = 11-1 = 10;

%e g_12(4) = b_13(10)-1 = 10-1 = 9;

%e g_13(4) = b_14(9)-1 = 9-1 = 8;

%e …

%e g_21(4) = 0;

%e So a(4)=11.

%o (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; }

%o 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

%Y Cf. A266203, A268688, A268689.

%K nonn,more

%O 0,3

%A _Natan Arie Consigli_, Apr 02 2016

%E a(6)-a(7) from _Michel Marcus_, Apr 04 2016