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

1,2

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)

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)

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

Prog

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

Crossrefs

Row 3 of A258207.

Setwise difference of A047241 \ A258016.

Cf. also A260440 (Every ninth term).

Sequence in context: A172367 A336234 A024901 * A000959 A204085 A230076

Adjacent sequences: A258008 A258009 A258010 * A258012 A258013 A258014

Keyword

nonn,easy

Author

Antti Karttunen, Jul 27 2015

Status

approved