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A054550 Composite numbers whose least prime factor is either 5 or 7. 1
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 (list; graph; refs; listen; history; text; internal format)
OFFSET
1,1
COMMENTS
Original definition: Union of 4 AP's: 25+30n, 35+30n, 49+42n, 77+42n.
LINKS
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
Sequence in context: A038509 A067793 A287918 * A107472 A193165 A060976
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

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Last modified March 28 05:39 EDT 2024. Contains 371235 sequences. (Running on oeis4.)