A306679 a(n) = round(1/(1-Integral_{x=0..1} f_n(x) dx)), where f_n is the n-th of all functions that are representable as x^x^...^x with m>=1 x's and parentheses inserted in all possible ways.

2, 5, 10, 2, 17, 6, 2, 4, 26, 13, 3, 5, 8, 2, 2, 4, 2, 37, 21, 8, 11, 15, 3, 5, 5, 6, 9, 6, 2, 2, 3, 2, 2, 4, 4, 2, 3, 50, 32, 16, 3, 19, 23, 7, 11, 2, 4, 7, 10, 12, 16, 13, 2, 3, 6, 3, 5, 5, 7, 6, 5, 9, 8, 6, 8, 2, 2, 2, 2, 2, 4, 2, 2, 2, 2, 2, 5, 4, 3, 4, 4

Offset: 1

Author

Alois P. Heinz, Mar 04 2019

Keywords

• nonn
• look

Comments

The ordering of the functions f_n is defined in A215703: f_1, f_2, ... = x, x^x, x^(x^2), x^(x^x), x^(x^3), x^(x^x*x), x^(x^(x^2)), x^(x^(x^x)), x^(x^4), x^(x^x*x^2), ... . Values of new records are in A322008.

Links

• Alois P. Heinz, Table of n, a(n) for n = 1..20299

Crossrefs

Cf. A000081, A087803, A215703, A322008.

Programs

Maple

T:= proc(n) T(n):=`if`(n=1, [x], map(h-> x^h, g(n-1$2))) end:
g:= proc(n, i) option remember; `if`(i=1, [x^n], [seq(seq(
      seq(mul(T(i)[w[t]-t+1], t=1..j)*v, v=g(n-i*j, i-1)), w=
      combinat[choose]([$1..nops(T(i))+j-1], j)), j=0..n/i)])
    end:
a:= proc() local i, l; i, l:= 0, []; proc(n) while n>
      nops(l) do i:= i+1; l:= [l[], map(f-> round(evalf(
      1/(1-int(f, x=0..1)))), T(i))[]] od; l[n] end
    end():
seq(a(n), n=1..100);

Formula

a(n) >= 2 for n >= 1.