A258011 - OEIS

%I #15 Apr 29 2022 10:58:33

%S 1,3,7,9,13,15,21,25,27,31,33,37,43,45,49,51,55,57,63,67,69,73,75,79,

%T 85,87,91,93,97,99,105,109,111,115,117,121,127,129,133,135,139,141,

%U 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

%N Numbers remaining after the third stage of Lucky sieve.

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

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

%H Antti Karttunen, <a href="/A258011/b258011.txt">Table of n, a(n) for n = 1..10000</a>

%H <a href="/index/Rec#order_13">Index entries for linear recurrences with constant coefficients</a>, signature (1,0,0,0,0,0,0,0,0,0,0,1,-1)

%F From _Jianing Song_, Apr 27 2022: (Start)

%F a(n) = a(n-12) + 42.

%F a(n) = a(n-1) + a(n-12) - a(n-13).

%F 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)

%p 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):

%p seq(coeff(ser, x, k), k = 1..74); # _Peter Luschny_, Apr 29 2022

%o (Scheme)

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

%Y Row 3 of A258207.

%Y Setwise difference of A047241 \ A258016.

%Y Cf. also A260440 (Every ninth term).

%K nonn,easy

%O 1,2

%A _Antti Karttunen_, Jul 27 2015