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

1,1

Comments

Original definition: Union of 4 AP's: 25+30n, 35+30n, 49+42n, 77+42n.

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).

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

Mathematica

Union[Flatten[Table[{30n+{25, 35}, 42n+{49, 77}}, {n, 0, 20}]]] (* Harvey P. Dale, Feb 19 2016 *)

Prog

(PARI) select( is_A054550(n)=vecsum((n=factor(n, 0))[, 2])>1&&n[1, 1]>=5, [0..550]) \\ M. F. Hasler, Nov 18 2018
(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

Crossrefs

Cf. A002808, A038509, A038511, A047229, A067793.

Sequence in context: A038509 A067793 A287918 * A107472 A193165 A060976

Adjacent sequences: A054547 A054548 A054549 * A054551 A054552 A054553

Keyword

nonn,easy

Author

Stuart M. Ellerstein (ellerstein(AT)aol.com), May 15 2000

Extensions

More terms from R. J. Mathar, Sep 30 2008

New name suggested by Andrew Howroyd, Nov 19 2018

Status

approved