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

5, 9, 15, 17, 19, 21, 23, 24, 25, 26, 27, 28, 29, 30, 31, 31, 31, 31, 31, 31, 31, 31, 31, 31, 31, 31, 31, 31, 31, 31, 31, 30, 29, 28, 27, 26, 25, 24, 23, 22, 21, 20, 19, 18, 17, 16, 15, 14, 13, 12, 11, 10, 9, 8, 7, 6, 5, 4, 3, 2, 1, 0

Offset

0,1

Comments

For more info see A266201-A266202.

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

Links

Table of n, a(n) for n=0..61.

Example

g_1(5) = b_2(5)-1 = b_2(2^2+1)-1 = 3^2+1-1 = 9;
g_2(5) = b_3(3^2)-1 = 4^2-1 = 15;
g_3(5) = b_4(3*4+3)-1 = 3*5+3-1 = 17;
g_4(5) = b_5(3*5 + 2)-1 = 3*6 + 2-1 = 19;
g_5(5) = b_6(3*6 + 1)-1 = 3*7+1-1 = 21;
g_6(5) = b_7(3*7)-1 = 3*8-1 = 23;
g_7(5) = b_8(2*8+7)-1 = 2*9+7-1 = 24;
g_8(5) = b_9(2*9+6)-1 = 2*10+6-1 = 25;
g_9(5) = b_10(2*10+5)-1 = 2*11+5-1 = 26;
g_10(5) = b_11(2*11+4)-1 = 2*12+4-1 = 27;
g_11(5) = b_12(2*12+3)-1 = 2*13+3-1 = 28;
g_12(5) = b_13(2*13+2)-1 = 2*14+2-1 = 29;
g_13(5) = b_14(2*14+1)-1 = 2*15+1-1 = 30;
g_14(5) = b_15(2*15)-1 = 2*16-1 = 31;
g_15(5) = b_16(16+15)-1 = 17+15-1 = 31;
...
g_30(5) = b_31(31)-1 = 31;
g_31(5) = b_32(31)-1 = 30;
g_32(5) = b_33(30)-1 = 29;
...
g_61(5) = 0. (End of sequence)

Mathematica

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 *)

Prog

(PARI) a(n, m=5) = { my(wn = m); for (k=2, n+1, wn = fromdigits(digits(wn, k), k+1) - 1); wn; }
vector(62, n, n--; a(n)) \\ Michel Marcus, Apr 03 2016 and Aug 08 2025

Crossrefs

Cf. A266204: G_n(5).

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.

Sequence in context: A314993 A314994 A106503 * A160593 A246156 A314995

Adjacent sequences: A267645 A267646 A267647 * A267649 A267650 A267651

Keyword

fini,nonn,full

Author

Natan Arie Consigli, Mar 17 2016

Extensions

Duplicated a(31) removed by Zhuorui He, Aug 07 2025

Status

approved