A260739 Column index to A255127: a(1) = 1; for n > 1, a(n) = the position at the stage where n is removed in the sieve which produces Ludic numbers.

1, 1, 1, 2, 1, 3, 1, 4, 2, 5, 1, 6, 1, 7, 3, 8, 1, 9, 2, 10, 4, 11, 1, 12, 1, 13, 5, 14, 1, 15, 2, 16, 6, 17, 3, 18, 1, 19, 7, 20, 1, 21, 1, 22, 8, 23, 1, 24, 4, 25, 9, 26, 1, 27, 2, 28, 10, 29, 3, 30, 1, 31, 11, 32, 5, 33, 1, 34, 12, 35, 1, 36, 2, 37, 13, 38, 1, 39, 6, 40, 14, 41, 1, 42, 4, 43, 15, 44, 1, 45, 1, 46, 16, 47, 7, 48, 1, 49, 17, 50, 2

Offset: 1

Author

Antti Karttunen, Jul 30 2015

Keywords

• nonn

Comments

Ordinal transform of A272565 (Ludic factor), and also of A260738. - Antti Karttunen, Apr 03 2018

Links

• Antti Karttunen, Table of n, a(n) for n = 1..10105

Crossrefs

Column index to array A255127.

Cf. A003309, A254100, A272565.

Cf. A260738 (corresponding row index).

Cf. A302035, A302036 (positions of terms that are powers of 2).

Cf. A078898, A246277, A260429, A260439 for column indices to other arrays similar to A255127.

Differs from A246277 (and also after the initial term from A078898) for the first time at n=19.

Programs

Scheme

(define (A260739 n) (cond ((= 1 n) 1) ((even? n) (/ n 2)) (else (let searchrow ((row 2)) (let searchcol ((col 1)) (cond ((>= (A255127bi row col) n) (if (= (A255127bi row col) n) col (searchrow (+ 1 row)))) (else (searchcol (+ 1 col))))))))) ;; Code for A255127bi given in A255127.

Formula

Other identities. For all n >= 2:

a(A003309(n)) = 1. [In Ludic sieve each Ludic number (after 1) is the first among the numbers removed at stage k.]

a(A254100(n)) = 2.

A255127(A260738(n), a(n)) = n.

For n > 1, A001511(a(n)) = A302035(n). - Antti Karttunen, Apr 03 2018

Extensions

Term a(1) changed from 0 to 1 to match with the definition of A078898 and the interpretation as an ordinal transform - Antti Karttunen, Apr 03 2018