A260437 -id:A260437 - cp's OEIS frontend

A260439 Column index to A255551: a(1) = 0; for n > 1: if n is Lucky number then a(n) = 1, otherwise for a(2k) = k, and for odd unlucky numbers, a(n) = 1 + the position at the stage where n is removed in the Lucky sieve.

0, 1, 1, 2, 2, 3, 1, 4, 1, 5, 3, 6, 1, 7, 1, 8, 4, 9, 2, 10, 1, 11, 5, 12, 1, 13, 2, 14, 6, 15, 1, 16, 1, 17, 7, 18, 1, 19, 3, 20, 8, 21, 1, 22, 2, 23, 9, 24, 1, 25, 1, 26, 10, 27, 2, 28, 3, 29, 11, 30, 4, 31, 1, 32, 12, 33, 1, 34, 1, 35, 13, 36, 1, 37, 1, 38, 14, 39, 1, 40, 5, 41, 15, 42, 2, 43, 1, 44, 16, 45, 4, 46, 1, 47, 17, 48, 3, 49, 1, 50, 18, 51, 6, 52, 1

Offset: 1

Antti Karttunen, Jul 29 2015

nonn

a(1) = 0, because 1 is outside of A255551 array proper.

Antti Karttunen, Table of n, a(n) for n = 1..10003

Cf. A000959, A050505, A145649, A255543, A255551.
Cf. also A260438 (corresponding row index).
Cf. A078898, A246277, A260429, A260437, A260739 for column indices to other arrays similar to A255551.

(define (A260439 n) (cond ((= 1 n) 0) ((not (zero? (A145649 n))) 1) ((even? n) (/ n 2)) (else (let searchrow ((row 2)) (let searchcol ((col 1)) (cond ((>= (A255543bi row col) n) (if (= (A255543bi row col) n) (+ 1 col) (searchrow (+ 1 row)))) (else (searchcol (+ 1 col))))))))) ;; Code for A255543bi given in A255543.

Other identities. For all n >= 1:
a(2n) = n.
Also, for all n >= 2:
A255551(A260438(n), a(n)) = n.
a(A219178(n)) = 2.

A260429 Column index to A255545: if n is Lucky number, then a(n) = 1, otherwise a(n) = 1 + the position at the stage where n is removed in the Lucky sieve.

Original entry on oeis.org

1, 2, 1, 3, 2, 4, 1, 5, 1, 6, 3, 7, 1, 8, 1, 9, 4, 10, 2, 11, 1, 12, 5, 13, 1, 14, 2, 15, 6, 16, 1, 17, 1, 18, 7, 19, 1, 20, 3, 21, 8, 22, 1, 23, 2, 24, 9, 25, 1, 26, 1, 27, 10, 28, 2, 29, 3, 30, 11, 31, 4, 32, 1, 33, 12, 34, 1, 35, 1, 36, 13, 37, 1, 38, 1, 39, 14, 40, 1, 41, 5, 42, 15, 43, 2, 44, 1, 45, 16, 46, 4, 47, 1, 48, 17, 49, 3, 50, 1, 51, 18, 52, 6, 53, 1

Offset: 1

Antti Karttunen, Jul 29 2015

nonn

Antti Karttunen, Table of n, a(n) for n = 1..10003

One more than A260437.
Cf. A000959, A050505, A145649, A219178, A255543, A255545.
Cf. also A260438 (corresponding row index).
Cf. A078898, A246277, A260439, A260739 for column indices to other arrays similar to A255545.

(define (A260429 n) (cond ((not (zero? (A145649 n))) 1) ((even? n) (+ 1 (/ n 2))) (else (let searchrow ((row 2)) (let searchcol ((col 1)) (cond ((>= (A255543bi row col) n) (if (= (A255543bi row col) n) (+ 1 col) (searchrow (+ 1 row)))) (else (searchcol (+ 1 col))))))))) ;; Code for A255543bi given in A255543.

Other identities. For all n >= 1:
a(n) = 1 + A260437(n).
Iff A145649(n) = 1, then a(n) = 1.
a(2n) = n+1. [Even numbers are removed at the stage one of the sieve, after 1 which is also removed in the beginning.]
a(A219178(n)) = 2.
A255545(A260438(n), a(n)) = n.

A265859 Unluckiness of n.

Original entry on oeis.org

0, 1, 0, 1, 2, 1, 0, 1, 0, 1, 2, 1, 0, 1, 0, 1, 2, 1, 3, 1, 0, 1, 2, 1, 0, 1, 4, 1, 2, 1, 0, 1, 0, 1, 2, 1, 0, 1, 3, 1, 2, 1, 0, 1, 5, 1, 2, 1, 0, 1, 0, 1, 2, 1, 6, 1, 4, 1, 2, 1, 3, 1, 0, 1, 2, 1, 0, 1, 0, 1, 2, 1, 0, 1, 0, 1, 2, 1, 0, 1, 3, 1, 2, 1, 7, 1, 0

Offset: 1

Max Barrentine, Dec 17 2015

nonn

If n is lucky, a(n)=0; if n is unlucky, a(n) is the step at which n is rejected from the lucky number sieve.

Max Barrentine, Table of n, a(n) for n = 1..10000

Cf. A000959, A050505, A145649, A260437, A260438.
Cf. also arrays A255543, A255545.
Cf. A271420 (analogous sequence).

(define (A265859 n) (* (- 1 (A145649 n)) (A260438 n))) ;; Antti Karttunen, Sep 11 2016

a(n) = (1-A145649(n)) * A260438(n). - Antti Karttunen, Sep 11 2016, corrected Nov 15 2019

cp's OEIS Frontend

A260439 Column index to A255551: a(1) = 0; for n > 1: if n is Lucky number then a(n) = 1, otherwise for a(2k) = k, and for odd unlucky numbers, a(n) = 1 + the position at the stage where n is removed in the Lucky sieve.

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A260429 Column index to A255545: if n is Lucky number, then a(n) = 1, otherwise a(n) = 1 + the position at the stage where n is removed in the Lucky sieve.

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A265859 Unluckiness of n.

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