A258016 -id:A258016 - cp's OEIS frontend

A260438 Row index to A255545: If n is k-th Lucky number then a(n) = k, otherwise a(n) = number of the stage where n is removed in Lucky sieve.

1, 1, 2, 1, 2, 1, 3, 1, 4, 1, 2, 1, 5, 1, 6, 1, 2, 1, 3, 1, 7, 1, 2, 1, 8, 1, 4, 1, 2, 1, 9, 1, 10, 1, 2, 1, 11, 1, 3, 1, 2, 1, 12, 1, 5, 1, 2, 1, 13, 1, 14, 1, 2, 1, 6, 1, 4, 1, 2, 1, 3, 1, 15, 1, 2, 1, 16, 1, 17, 1, 2, 1, 18, 1, 19, 1, 2, 1, 20, 1, 3, 1, 2, 1, 7, 1, 21, 1, 2, 1, 4, 1, 22, 1, 2, 1, 5, 1, 23, 1, 2, 1, 3, 1, 24, 1, 2, 1, 8, 1, 25, 1, 2, 1, 26, 1, 6, 1, 2, 1

Offset: 1

Antti Karttunen, Jul 29 2015

nonn

For n >= 2 this works also as a row index to array A255551 (which does not contain 1) and when restricted to unlucky numbers, A050505, also as a row index to array A255543.

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

Cf. A000959, A050505, A109497, A145649, A219178, A255543, A255545, A255551.
Cf. also A260429, A260439 (corresponding column indices).
Cf. A055396, A260738 for row indices to other arrays similar to A255545.

(define (A260438 n) (cond ((not (zero? (A145649 n))) (A109497 n)) ((even? n) 1) (else (let searchrow ((row 2)) (let searchcol ((col 1)) (cond ((>= (A255543bi row col) n) (if (= (A255543bi row col) n) row (searchrow (+ 1 row)))) (else (searchcol (+ 1 col))))))))) ;; Code for A255543bi given in A255543.

Other identities. For all n >= 1:
a(A000959(n)) = n.
a(A219178(n)) = n.
a(2n) = 1. [All even numbers are removed at the stage one of the sieve.]
a(A016969(n)) = 2.
a(A258016(n)) = 3.
a(A260440(n)) = 4.
A255545(a(n), A260429(n)) = n.
For all n >= 2, A255551(a(n), A260439(n)) = n.

A258011 Numbers remaining after the third stage of Lucky sieve.

Original entry on oeis.org

1, 3, 7, 9, 13, 15, 21, 25, 27, 31, 33, 37, 43, 45, 49, 51, 55, 57, 63, 67, 69, 73, 75, 79, 85, 87, 91, 93, 97, 99, 105, 109, 111, 115, 117, 121, 127, 129, 133, 135, 139, 141, 147, 151, 153, 157, 159, 163, 169, 171, 175, 177, 181, 183, 189, 193, 195, 199, 201, 205, 211, 213, 217, 219, 223, 225, 231, 235, 237, 241, 243, 247, 253, 255

Offset: 1

Antti Karttunen, Jul 27 2015

Equal to A047241 with its every seventh term (A258016) removed.

Numbers congruent to {1, 3, 7, 9, 13, 15, 21, 25, 27, 31, 33, 37} modulo 42. - Jianing Song, Apr 27 2022

Antti Karttunen, Table of n, a(n) for n = 1..10000
Index entries for linear recurrences with constant coefficients, signature (1,0,0,0,0,0,0,0,0,0,0,1,-1)

Row 3 of A258207.
Setwise difference of A047241 \ A258016.
Cf. also A260440 (Every ninth term).

gf := (x*(1 + x*(2 + x*(4 + x*(2 + x*(4 + x*(2 + x*(6 + x*(4 + x*(2 + x*(4 + x*(2 + x*(4 + 5*x)))))))))))))/(1 - x*(1 + (1 - x)*x^11)): ser:= series(gf, x, 112):
seq(coeff(ser, x, k), k = 1..74); # Peter Luschny, Apr 29 2022

(define (A258011 n) (A258207bi 3 n)) ;; A258207bi given in A258207.

From Jianing Song, Apr 27 2022: (Start)
a(n) = a(n-12) + 42.
a(n) = a(n-1) + a(n-12) - a(n-13).
G.f.:(x+2*x^2+4*x^3+2*x^4+4*x^5+2*x^6+6*x^7+4*x^8+2*x^9+4*x^10+2*x^11+4*x^12+5*x^13)/(1-x-x^12+x^13). (End)

cp's OEIS Frontend

A260438 Row index to A255545: If n is k-th Lucky number then a(n) = k, otherwise a(n) = number of the stage where n is removed in Lucky sieve.

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