A258011 Numbers remaining after the third stage of Lucky sieve.

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

Author

Antti Karttunen, Jul 27 2015

Keywords

• nonn
• easy

Comments

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

Links

• 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)

Crossrefs

Row 3 of A258207.

Setwise difference of A047241 \ A258016.

Cf. also A260440 (Every ninth term).

Programs

Maple

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

Scheme

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

Formula

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)