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

1,1

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

Formula

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

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);

Crossrefs

Cf. A000081, A087803, A215703, A322008.

Sequence in context: A083460 A172411 A264784 * A125974 A218336 A059955

Adjacent sequences: A306676 A306677 A306678 * A306680 A306681 A306682

Keyword

nonn,look

Author

Alois P. Heinz, Mar 04 2019

Status

approved