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 A254310 a(n) = 3[0]3[1]3...3[n-1]3[n]3 where [n] is the n-th hyperoperator. 4
 3, 4, 7, 13, 85 (list; graph; refs; listen; history; text; internal format)
 OFFSET -1,1 COMMENTS x[n]y = H_n(x,y) is the aggregation of x and y using the n-th hyperoperator. See A054871 for hyperoperator definitions and key links. In a(-1) no hyperoperator is applied to 3 so a(-1) = 3. For n>0 calculate the chain a(n) = 3[0]3[1]3...3[n-1]3[n]3. Hyperoperators of higher degree have the higher aggregation priority, so tetration before exponentiation, exponentiation before multiplication, multiplication before addition, etc. LINKS Wikipedia, Hyperoperation. FORMULA a(-1) = 3, a(n) = 3[0]3[1]3...3[n-1]3[n]3. EXAMPLE a(0) = 3[0]3 = '3 = 4; a(1) = 3[0]3[1]3 = '3+3 = 7; a(2) = 3[0]3[1]3[2]3 = '3+3*3 = 13; a(3) = 3[0]3[1]3[2]3[3]3 = '3+3*3^3 = 85; a(4) > 3^7625597484988 (a 3638334640025-digit number). PROG (PARI) f(x, y, o) = {if (o==4, z=x; for (i=1, y-1, z = x^z); return (z)); if (o==3, return(x^y)); if (o==2, return(x*y)); if (o==1, return(x+y)); } a(n) = {t = 3; if (n>4, return("too big")); if (n==-1, return(t)); v = vector(n+1, k, t); w = vector(n+1, k, n-k+1); x = v[1]; for (k=1, n+1, if (w[k], x = f(v[k+1], x, w[k]), x = x+1); ); x; } \\ Michel Marcus, Jul 29 2015 CROSSREFS Cf. A000012 (0[0]0[1]...[n]0), A157532 (1[0]1[1]...[n]1), A254225 (2[0]2[1]...[n]2). Cf. A054871. Sequence in context: A282718 A092406 A250297 * A121174 A050071 A041002 Adjacent sequences:  A254307 A254308 A254309 * A254311 A254312 A254313 KEYWORD nonn,less AUTHOR Natan Arie Consigli, May 03 2015 STATUS approved

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Last modified May 14 19:53 EDT 2021. Contains 343903 sequences. (Running on oeis4.)