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 A286594 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 = A000203(n). 8
 0, 2, 3, 4, 5, 1, 7, 8, 6, 5, 11, 4, 13, 5, 4, 16, 17, 7, 19, 11, 12, 6, 23, 3, 10, 6, 15, 1, 29, 5, 31, 32, 7, 7, 9, 13, 37, 7, 9, 5, 41, 6, 43, 11, 7, 8, 47, 7, 14, 14, 7, 11, 53, 7, 11, 8, 15, 9, 59, 6, 61, 9, 12, 64, 10, 8, 67, 11, 8, 20, 71, 9, 73, 10, 13, 9, 23, 9, 79, 17, 42, 11, 83, 4, 11, 11, 8, 23, 89, 5, 7, 9, 16, 12, 8, 6, 97, 17, 9, 16, 101, 11 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,2 LINKS Antti Karttunen, Table of n, a(n) for n = 1..10000 Antti Karttunen, Scheme (Racket) program to compute this sequence FORMULA a(n) = A285721(n, A000203(n)) = A285721(A000203(n), n). a(n) = n - A300237(n). - Antti Karttunen, Mar 02 2018 EXAMPLE For n = 1, sigma(1) = 1, and the arguments for gcd are equal at the start, thus a(1) = 0. For n = 2, sigma(2) = 3, gcd(3,2) = gcd(2,1) = gcd(1,1), thus 2 steps were required to reach the termination condition, and a(2) = 2. For n = 6, sigma(6) = 12, gcd(12,6) = gcd(6,6), thus a(6) = 1. For n = 9, sigma(9) = 13, gcd(13,9) = gcd(9,4) = gcd(5,4) = gcd(4,1) = gcd(3,1) = gcd(2,1) = gcd(1,1), thus a(9) = 6. Here the simple subtracting version of gcd-algorithm is used, where the new arguments will be the smaller argument and the smaller argument subtracted from the larger, and this is repeated until both are equal. PROG (Scheme) (define (A286594 n) (A285721bi n (A000203 n))) ;; Requires also code from A000203 and A285721. (Python) from sympy import divisor_sigma def A(n, k): return 0 if n==k else 1 + A(abs(n - k), min(n, k)) def a(n): return A(n, divisor_sigma(n)) # Indranil Ghosh, May 22 2017 (PARI) A285721(n, k) = if(n==k, 0, 1 + A285721(abs(n-k), min(n, k))); A286594(n) = A285721(n, sigma(n)); \\ Antti Karttunen, Mar 02 2018 CROSSREFS Cf. A000203, A009194, A285721. Cf. A000396 (positions of 1's). Cf. also A300227, A300228, A300234, A300237, A300238. Sequence in context: A081806 A059806 A332425 * A241479 A100994 A140523 Adjacent sequences:  A286591 A286592 A286593 * A286595 A286596 A286597 KEYWORD nonn AUTHOR Antti Karttunen, May 21 2017 STATUS approved

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Last modified July 24 20:26 EDT 2021. Contains 346273 sequences. (Running on oeis4.)