cp's OEIS Frontend

A054550 Composite numbers whose least prime factor is either 5 or 7.

%I A054550 #24 Nov 19 2018 21:01:59
%S A054550 25,35,49,55,65,77,85,91,95,115,119,125,133,145,155,161,175,185,203,
%T A054550 205,215,217,235,245,259,265,275,287,295,301,305,325,329,335,343,355,
%U A054550 365,371,385,395,413,415,425,427,445,455,469,475,485,497,505,511,515,535
%N A054550 Composite numbers whose least prime factor is either 5 or 7.
%C A054550 Original definition: Union of 4 AP's: 25+30n, 35+30n, 49+42n, 77+42n.
%H A054550 Harvey P. Dale, <a href="/A054550/b054550.txt">Table of n, a(n) for n = 1..1000</a>
%H A054550 <a href="/index/Rec#order_23">Index entries for linear recurrences with constant coefficients</a>, signature (1,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,-1).
%F A054550 a(n) = a(n-1) + a(n-22) - a(n-23). - _Charles R Greathouse IV_, Jun 01 2018
%F A054550 G.f.: x*(25 + 10*x + 14*x^2 + 6*x^3 + 10*x^4 + 12*x^5 + 8*x^6 + 6*x^7 + 4*x^8 + 20*x^9 + 4*x^10 + 6*x^11 + 8*x^12 + 12*x^13 + 10*x^14 + 6*x^15 + 14*x^16 + 10*x^17 + 18*x^18 + 2*x^19 + 10*x^20 + 2*x^21 - 7*x^22) / ((1 - x)^2*(1 + x)*(1 - x + x^2 - x^3 + x^4 - x^5 + x^6 - x^7 + x^8 - x^9 + x^10)*(1 + x + x^2 + x^3 + x^4 + x^5 + x^6 + x^7 + x^8 + x^9 + x^10)). - _Colin Barker_, Nov 19 2018
%t A054550 Union[Flatten[Table[{30n+{25,35},42n+{49,77}},{n,0,20}]]] (* _Harvey P. Dale_, Feb 19 2016 *)
%o A054550 (PARI) select( is_A054550(n)=vecsum((n=factor(n,0))[,2])>1&&n[1,1]>=5, [0..550]) \\ _M. F. Hasler_, Nov 18 2018
%o A054550 (PARI) Vec(x*(25 + 10*x + 14*x^2 + 6*x^3 + 10*x^4 + 12*x^5 + 8*x^6 + 6*x^7 + 4*x^8 + 20*x^9 + 4*x^10 + 6*x^11 + 8*x^12 + 12*x^13 + 10*x^14 + 6*x^15 + 14*x^16 + 10*x^17 + 18*x^18 + 2*x^19 + 10*x^20 + 2*x^21 - 7*x^22) / ((1 - x)^2*(1 + x)*(1 - x + x^2 - x^3 + x^4 - x^5 + x^6 - x^7 + x^8 - x^9 + x^10)*(1 + x + x^2 + x^3 + x^4 + x^5 + x^6 + x^7 + x^8 + x^9 + x^10)) + O(x^60)) \\ _Colin Barker_, Nov 19 2018
%Y A054550 Cf. A002808, A038509, A038511, A047229, A067793.
%K A054550 nonn,easy
%O A054550 1,1
%A A054550 Stuart M. Ellerstein (ellerstein(AT)aol.com), May 15 2000
%E A054550 More terms from _R. J. Mathar_, Sep 30 2008
%E A054550 New name suggested by _Andrew Howroyd_, Nov 19 2018