A278528 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).

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, 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, 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

Offset: 1

Author

Antti Karttunen, Nov 23 2016

Keywords

• nonn

Comments

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).

Links

• Antti Karttunen, Table of n, a(n) for n = 1..10707
• Index entries for sequences related to the Josephus Problem

Crossrefs

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

Cf. A000960 (positions of zeros).

Programs

Scheme

;; Very crude. Find it with two nested loops. (Maybe a closed form exists?)
(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)))))))))
;; Code for A278507bi given in A278507.

Formula

Conjecture: a(n) = [C > 0] * C where we start with A := n, B := n - 1, C, m := 0 and until A = B consecutively apply m := m + 1, C := A - B, A := abs(A - m - (A mod m)), B := abs(B - m - (B mod m)). - Mikhail Kurkov, May 19 2025