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A267648 a(n) = g_n(5) where g is the function defined in A266202.

%I A267648 #28 Aug 14 2025 18:55:56
%S A267648 5,9,15,17,19,21,23,24,25,26,27,28,29,30,31,31,31,31,31,31,31,31,31,
%T A267648 31,31,31,31,31,31,31,31,30,29,28,27,26,25,24,23,22,21,20,19,18,17,16,
%U A267648 15,14,13,12,11,10,9,8,7,6,5,4,3,2,1,0
%N A267648 a(n) = g_n(5) where g is the function defined in A266202.
%C A267648 For more info see A266201-A266202.
%C A267648 This sequence has A266203(5)+1=62 terms and a(A266203(5))=a(61)=0 is the last term of this sequence. The maximum term in this sequence is a((A266203(5)-1)/2)=a(30)=(A266203(5)+1)/2=31. - _Zhuorui He_, Aug 08 2025
%e A267648 g_1(5) = b_2(5)-1 = b_2(2^2+1)-1 = 3^2+1-1 = 9;
%e A267648 g_2(5) = b_3(3^2)-1 = 4^2-1 = 15;
%e A267648 g_3(5) = b_4(3*4+3)-1 = 3*5+3-1 = 17;
%e A267648 g_4(5) = b_5(3*5 + 2)-1 = 3*6 + 2-1 = 19;
%e A267648 g_5(5) = b_6(3*6 + 1)-1 = 3*7+1-1 = 21;
%e A267648 g_6(5) = b_7(3*7)-1 = 3*8-1 = 23;
%e A267648 g_7(5) = b_8(2*8+7)-1 = 2*9+7-1 = 24;
%e A267648 g_8(5) = b_9(2*9+6)-1 = 2*10+6-1 = 25;
%e A267648 g_9(5) = b_10(2*10+5)-1 = 2*11+5-1 = 26;
%e A267648 g_10(5) = b_11(2*11+4)-1 = 2*12+4-1 = 27;
%e A267648 g_11(5) = b_12(2*12+3)-1 = 2*13+3-1 = 28;
%e A267648 g_12(5) = b_13(2*13+2)-1 = 2*14+2-1 = 29;
%e A267648 g_13(5) = b_14(2*14+1)-1 = 2*15+1-1 = 30;
%e A267648 g_14(5) = b_15(2*15)-1 = 2*16-1 = 31;
%e A267648 g_15(5) = b_16(16+15)-1 = 17+15-1 = 31;
%e A267648 ...
%e A267648 g_30(5) = b_31(31)-1 = 31;
%e A267648 g_31(5) = b_32(31)-1 = 30;
%e A267648 g_32(5) = b_33(30)-1 = 29;
%e A267648 ...
%e A267648 g_61(5) = 0. (End of sequence)
%t A267648 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, 5], {n, 0, 61}] (* _Michael De Vlieger_, May 17 2016 *)
%o A267648 (PARI) a(n, m=5) = { my(wn = m); for (k=2, n+1, wn = fromdigits(digits(wn, k), k+1) - 1); wn; }
%o A267648 vector(62, n, n--; a(n)) \\ _Michel Marcus_, Apr 03 2016 and Aug 08 2025
%Y A267648 Cf. A266204: G_n(5).
%Y A267648 Weak Goodstein sequences: A137411: g_n(11); A265034: g_n(266); A267647: g_n(4); A266202: g_n(n); A266203: a(n) = k such that g_k(n)=0.
%K A267648 fini,nonn,full
%O A267648 0,1
%A A267648 _Natan Arie Consigli_, Mar 17 2016
%E A267648 Duplicated a(31) removed by _Zhuorui He_, Aug 07 2025