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%I #60 Dec 08 2020 03:49:35
%S 11,121,143,187,209,253,319,341,407,451,473,517,583,649,671,737,781,
%T 803,869,913,979,1067,1111,1133,1177,1199,1243,1331,1397,1441,1507,
%U 1529,1573,1639,1661,1727,1793,1837,1859,1903,1969,1991,2057,2101,2123,2167,2189,2299,2321
%N Numbers whose smallest prime factor is 11.
%C Fifth row of A083140.
%C Integers k such that gcd(11*k, 210) = 1.
%H Amiram Eldar, <a href="/A084969/b084969.txt">Table of n, a(n) for n = 1..10000</a>
%H <a href="/index/Rec#order_49">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, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, -1).
%F G.f.: 11*x*(x^48 +10*x^47 +2*x^46 +4*x^45 +2*x^44 +4*x^43 +6*x^42 +2*x^41 +6*x^40 +4*x^39 +2*x^38 +4*x^37 +6*x^36 +6*x^35 +2*x^34 +6*x^33 +4*x^32 +2*x^31 +6*x^30 +4*x^29 +6*x^28 +8*x^27 +4*x^26 +2*x^25 +4*x^24 +2*x^23 +4*x^22 +8*x^21 +6*x^20 +4*x^19 +6*x^18 +2*x^17 +4*x^16 +6*x^15 +2*x^14 +6*x^13 +6*x^12 +4*x^11 +2*x^10 +4*x^9 +6*x^8 +2*x^7 +6*x^6 +4*x^5 +2*x^4 +4*x^3 +2*x^2 +10*x +1) / (x^49 -x^48 -x +1). - _Colin Barker_, Feb 22 2013
%F a(n) = a(n-48) + 2310 = a(n-1) + a(n-48) - a(n-49). - _Charles R Greathouse IV_, Nov 19 2014
%F Lim_{n->infinity} a(n)/n = A038111(5)/A038110(5) = 385/8 = 48.125. - _Vladimir Shevelev_, Jan 20 2015
%F a(n) = 11*A008364(n).
%e a(2) = 11*11, a(3) = 11*13.
%t 11Select[ Range[210], GCD[ #, 2*3*5*7] == 1 & ]
%t Select[11*Range[0,200],GCD[#,210]==1&] (* _Harvey P. Dale_, Dec 23 2013 *)
%o (PARI) is(n)=gcd(n,2310)==11 \\ _Charles R Greathouse IV_, Nov 19 2014
%Y Cf. A084967 (5), A084968 (7), A084970 (13), A332799 (17), A332798 (19), A332797 (23), A008364 (11-rough numbers).
%Y Cf. A008364, A038110, A038111, A083140.
%K nonn,easy
%O 1,1
%A _Robert G. Wilson v_, Jun 15 2003
%E a(47)-a(49) from _Georg Fischer_, Nov 07 2019
%E New name from _Frank Ellermann_, Feb 25 2020
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