A260738 - OEIS

%I #15 Aug 02 2015 17:54:48

%S 0,1,2,1,3,1,4,1,2,1,5,1,6,1,2,1,7,1,3,1,2,1,8,1,9,1,2,1,10,1,4,1,2,1,

%T 3,1,11,1,2,1,12,1,13,1,2,1,14,1,3,1,2,1,15,1,5,1,2,1,4,1,16,1,2,1,3,

%U 1,17,1,2,1,18,1,6,1,2,1,19,1,3,1,2,1,20,1,4,1,2,1,21,1,22,1,2,1,3,1,23,1,2,1,7,1,5,1,2,1,24,1,3,1,2,1,4,1,25,1,2,1,26,1

%N Row index to A255127: a(1) = 0; for n > 1, a(n) = number of the stage where n is removed in the sieve which produces Ludic numbers.

%H Antti Karttunen, <a href="/A260738/b260738.txt">Table of n, a(n) for n = 1..10105</a>

%F Other identities. For all n >= 1:

%F a(A003309(n)) = n-1. [In Ludic sieve A003309(k+1) (i.e., the k-th Ludic number after 1) is the first among the numbers removed at stage k.]

%F a(2n) = 1. [All even numbers are removed at the stage one of the sieve.]

%F a(A016945(n)) = 2, a(A255413(n)) = 3, a(A255414(n)) = 4, ..., a(A255419(n)) = 9.

%F a(A254100(n)) = n.

%F For all n >= 2:

%F A255127(a(n), A260739(n)) = n.

%o (Scheme)

%o (define (A260738 n) (cond ((= 1 n) 0) ((even? n) 1) (else (let searchrow ((row 2)) (let searchcol ((col 1)) (cond ((>= (A255127bi row col) n) (if (= (A255127bi row col) n) row (searchrow (+ 1 row)))) (else (searchcol (+ 1 col))))))))) ;; Code for A255127bi given in A255127.

%Y Row index to array A255127.

%Y Cf. A003309, A254100.

%Y Cf. A260739 (corresponding column index).

%Y Cf. A055396, A260438 for row indices to other arrays similar to A255127.

%Y Differs from A055396 for the first time at n=19.

%K nonn

%O 1,3

%A _Antti Karttunen_, Jul 30 2015