

A300234


a(n) = number of steps in simple Euclidean algorithm for gcd(n,k) to reach the termination test n=k when starting with n = n and k = phi(n).


6



0, 1, 2, 1, 4, 2, 6, 1, 2, 3, 10, 2, 12, 4, 8, 1, 16, 2, 18, 3, 4, 6, 22, 2, 4, 7, 2, 4, 28, 6, 30, 1, 9, 9, 9, 2, 36, 10, 5, 3, 40, 4, 42, 6, 8, 12, 46, 2, 6, 3, 10, 7, 52, 2, 5, 4, 6, 15, 58, 6, 60, 16, 4, 1, 10, 8, 66, 9, 11, 13, 70, 2, 72, 19, 8, 10, 13, 6, 78, 3, 2, 21, 82, 4, 24, 22, 12, 6, 88, 6, 11, 12, 8, 24, 13, 2, 96, 4, 9, 3, 100, 10, 102, 7, 9
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OFFSET

1,3


LINKS

Antti Karttunen, Table of n, a(n) for n = 1..65537
Antti Karttunen, Scheme (Racket) program to compute this sequence


FORMULA

a(n) = A285721(n,A000010(n)).
a(n) = n  A300238(n).


EXAMPLE

For n = 1, phi(1) = 1, and the arguments for gcd are equal at the start, thus a(1) = 0.
For n = 2, eulerphi(2) = 1, gcd(2,1) = gcd(1,1), thus 1 step were required to reach the termination condition, and a(2) = 1.
For n = 5, eulerphi(5) = 4, gcd(5,4) = gcd(4,1) = gcd(3,1) = gcd(2,1) = gcd(1,1), four steps required, thus a(5) = 4.
For n = 6, eulerphi(6) = 2, gcd(6,2) = gcd(4,2) = gcd(2,2), two steps required, thus a(6) = 2.
Here a simple subtracting version of gcdalgorithm is used, where the new versions of two arguments will be the smaller argument and the smaller argument subtracted from the larger, and this is repeated until both are equal.


PROG

(PARI)
A285721(n, k) = if(n==k, 0, 1 + A285721(abs(nk), min(n, k)));
A300234(n) = A285721(n, eulerphi(n));


CROSSREFS

Cf. A000010, A285721.
Cf. also A286594, A300227, A300228, A300237, A300238.
Sequence in context: A057923 A147763 A098371 * A070777 A173614 A173557
Adjacent sequences: A300231 A300232 A300233 * A300235 A300236 A300237


KEYWORD

nonn


AUTHOR

Antti Karttunen, Mar 02 2018


STATUS

approved



