A190951 - OEIS

A190951

Closest integer to the largest real number x such that exp(x) = x^n, for n>=3.

5, 9, 13, 17, 21, 26, 31, 36, 41, 46, 51, 56, 62, 67, 73, 79, 84, 90, 96, 102, 108, 114, 120, 126, 132, 138, 144, 150, 157, 163, 169, 176, 182, 189, 195, 202, 208, 215, 221, 228, 235, 241, 248, 255, 262, 268, 275, 282, 289, 296, 303, 310, 317, 324, 331, 338, 345, 352

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OFFSET

3,1

COMMENTS

n=3 is the starting index because exp(x) > x^n for all x>=0 when n=1,2.

LINKS

Table of n, a(n) for n=3..60.

MATHEMATICA

a[n_] := Round[ E^-ProductLog[-1, -1/n]]; Table[a[n], {n, 3, 60}]

CROSSREFS

Cf. A088346 (Smallest integer k where exp(x)>x^n for all x>=k).

Cf. A190952 (Largest integer k for which exp(k) < k^n).