A054550 Composite numbers whose least prime factor is either 5 or 7.
25, 35, 49, 55, 65, 77, 85, 91, 95, 115, 119, 125, 133, 145, 155, 161, 175, 185, 203, 205, 215, 217, 235, 245, 259, 265, 275, 287, 295, 301, 305, 325, 329, 335, 343, 355, 365, 371, 385, 395, 413, 415, 425, 427, 445, 455, 469, 475, 485, 497, 505, 511, 515, 535
Offset: 1
Links
- Harvey P. Dale, Table of n, a(n) for n = 1..1000
- Index entries for linear recurrences with constant coefficients, signature (1,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,-1).
Programs
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Mathematica
Union[Flatten[Table[{30n+{25,35},42n+{49,77}},{n,0,20}]]] (* Harvey P. Dale, Feb 19 2016 *) -
PARI
select( is_A054550(n)=vecsum((n=factor(n,0))[,2])>1&&n[1,1]>=5, [0..550]) \\ M. F. Hasler, Nov 18 2018
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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
Formula
a(n) = a(n-1) + a(n-22) - a(n-23). - Charles R Greathouse IV, Jun 01 2018
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
Extensions
More terms from R. J. Mathar, Sep 30 2008
New name suggested by Andrew Howroyd, Nov 19 2018
Comments