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%I #62 Jan 11 2020 15:57:46
%S 3,4,7,13,85
%N a(n) = 3[0]3[1]3...3[n-1]3[n]3 where [n] is the n-th hyperoperator.
%C 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.
%C 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.
%H Wikipedia, <a href="https://en.wikipedia.org/wiki/Hyperoperation">Hyperoperation</a>.
%H <a href="/index/Ho">Index Section Ho-Hy</a>
%F a(-1) = 3, a(n) = 3[0]3[1]3...3[n-1]3[n]3.
%e a(0) = 3[0]3 = '3 = 4;
%e a(1) = 3[0]3[1]3 = '3+3 = 7;
%e a(2) = 3[0]3[1]3[2]3 = '3+3*3 = 13;
%e a(3) = 3[0]3[1]3[2]3[3]3 = '3+3*3^3 = 85;
%e a(4) > 3^7625597484988 (a 3638334640025-digit number).
%o (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));}
%o 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
%Y Cf. A000012 (0[0]0[1]...[n]0), A157532 (1[0]1[1]...[n]1), A254225 (2[0]2[1]...[n]2).
%Y Cf. A054871.
%K nonn,less
%O -1,1
%A _Natan Arie Consigli_, May 03 2015
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