A364127 - OEIS

A364127

The number of trailing 0's in the Stolarsky representation of n (A364121).

0, 0, 1, 0, 0, 1, 0, 2, 0, 0, 1, 0, 1, 0, 0, 2, 0, 0, 1, 0, 3, 0, 0, 1, 0, 1, 0, 0, 2, 0, 0, 1, 0, 2, 0, 0, 1, 0, 0, 1, 0, 3, 0, 0, 1, 0, 1, 0, 0, 2, 0, 0, 1, 0, 4, 0, 0, 1, 0, 0, 1, 0, 2, 0, 0, 1, 0, 2, 0, 0, 1, 0, 0, 1, 0, 3, 0, 0, 1, 0, 1, 0, 0, 2, 0, 0, 1

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OFFSET

2,8

COMMENTS

The first position of k = 2, 3, 4, ... is A055588(k+1).

The asymptotic density of the occurrences of k = 0, 1, 2, ... is (2-phi)^k/phi, where phi is the golden ratio (A001622).

The asymptotic mean of this sequence is phi - 1 (A094214) and the asymptotic standard deviation is 1.

LINKS

Amiram Eldar, Table of n, a(n) for n = 2..10000

FORMULA

a(n) = A122840(A364121(n)).

MATHEMATICA

stol[n_] := stol[n] = If[n == 1, {}, If[n != Round[Round[n/GoldenRatio]*GoldenRatio], Join[stol[Floor[n/GoldenRatio^2] + 1], {0}], Join[stol[Round[n/GoldenRatio]], {1}]]];

a[n_] := IntegerExponent[FromDigits[stol[n]], 10]; Array[a, 100, 2]

PROG

(PARI) stol(n) = {my(phi=quadgen(5)); if(n==1, [], if(n != round(round(n/phi)*phi), concat(stol(floor(n/phi^2) + 1), [0]), concat(stol(round(n/phi)), [1]))); }

a(n) = valuation(fromdigits(stol(n)), 10);

CROSSREFS

Cf. A001622, A055588, A094214, A122840, A364121.

Sequence in context: A325414 A216510 A005089 * A340999 A119395 A087476

Adjacent sequences: A364124 A364125 A364126 * A364128 A364129 A364130

KEYWORD

nonn,base

AUTHOR

Amiram Eldar, Jul 07 2023

STATUS

approved

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