A329056 a(n) is the integer nearest to the result of raising n to the power of the fraction that is the natural logarithm of n over the natural logarithm of the golden ratio.

1, 3, 12, 54, 218, 790, 2614, 7989, 22756, 60950, 154631, 373880, 866019, 1930121, 4154593, 8664718, 17557769, 34651632, 66747915, 125725045, 231949573, 419750808, 746081780, 1304039046, 2243705012, 3803904385, 6360060015, 10495565911, 17107197521

Offset

1,2

Links

Table of n, a(n) for n=1..29.

Formula

a(n) = round(n^(log(n)/log(phi))).

Prog

(JavaScript)
var listy = [];
for (var i = 1; i < 30; i++) {
var u = Math.round(Math.pow(i, Math.log(i)/Math.log(((Math.sqrt(5)+1)/2))));
appendItem(listy, u);
}
console.log(listy);
(PARI) vector(30, n, round(n^(log(n)/log((sqrt(5) + 1)/2)))) \\ Andrew Howroyd, Nov 02 2019

Crossrefs

Cf. A001622.

Sequence in context: A120983 A124810 A370821 * A191577 A282901 A123348

Adjacent sequences: A329053 A329054 A329055 * A329057 A329058 A329059

Keyword

nonn

Author

Sebastian F. Orellana, Nov 02 2019

Status

approved