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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. 3
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 (list; graph; refs; listen; history; text; internal format)
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

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Last modified September 23 21:27 EDT 2020. Contains 337315 sequences. (Running on oeis4.)