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

1,5

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

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

Prog

(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.

Crossrefs

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

Cf. A000960 (positions of zeros).

Sequence in context: A279928 A297325 A375466 * A257261 A355141 A171963

Adjacent sequences: A278525 A278526 A278527 * A278529 A278530 A278531

Keyword

nonn

Author

Antti Karttunen, Nov 23 2016

Status

approved