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a(n) = number of the round in which n is removed in the Flavius sieve, 0 if it is never removed (when n is one of the terms of A000960).
4

%I #28 Apr 25 2024 10:33:17

%S 0,1,0,1,2,1,0,1,3,1,2,1,0,1,4,1,2,1,0,1,3,1,2,1,5,1,0,1,2,1,6,1,3,1,

%T 2,1,4,1,0,1,2,1,7,1,3,1,2,1,0,1,5,1,2,1,4,1,3,1,2,1,8,1,0,1,2,1,9,1,

%U 3,1,2,1,6,1,4,1,2,1,0,1,3,1,2,1,5,1,10,1,2,1,0,1,3,1,2,1,4,1,7,1,2,1,11,1,3,1,2,1,0,1,5,1,2,1,4,1,3,1,2,1

%N a(n) = number of the round in which n is removed in the Flavius sieve, 0 if it is never removed (when n is one of the terms of A000960).

%C a(n) = index of the row where n is located in array A278507, 0 if n does not occur there (when n is one of the terms of A000960).

%H Antti Karttunen, <a href="/A278528/b278528.txt">Table of n, a(n) for n = 1..10707</a>

%H <a href="/index/J#Josephus">Index entries for sequences related to the Josephus Problem</a>

%o (Scheme)

%o ;; Very crude. Find it with two nested loops. (Maybe a closed form exists?)

%o (define (A278528 n) (cond ((not (zero? (A278169 n))) 0) ((even? n) 1) (else (let searchrow ((row 2)) (let searchcol ((col 1)) (cond ((>= (A278507bi row col) n) (if (= (A278507bi row col) n) row (searchrow (+ 1 row)))) (else (searchcol (+ 1 col)))))))))

%o ;; Code for A278507bi given in A278507.

%Y Cf. A278507, A278529 (the other index), A278538.

%Y Cf. A000960 (positions of zeros).

%K nonn

%O 1,5

%A _Antti Karttunen_, Nov 23 2016