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 A267648 a(n) = g_n(5) where g is the function defined in A266202. 9
 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, 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 (list; graph; refs; listen; history; text; internal format)
 OFFSET 0,1 COMMENTS For more info see A266201-A266202. LINKS 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) = {if (n == 0, return (5)); wn = 5; for (k=2, n+1, pd = Pol(digits(wn, k)); wn = subst(pd, x, k+1) - 1; ); wn; } vector(62, n, n--; a(n)) \\ Michel Marcus, Apr 03 2016 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 STATUS approved

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Last modified October 26 03:21 EDT 2020. Contains 338027 sequences. (Running on oeis4.)