A084969 Numbers whose smallest prime factor is 11.

11, 121, 143, 187, 209, 253, 319, 341, 407, 451, 473, 517, 583, 649, 671, 737, 781, 803, 869, 913, 979, 1067, 1111, 1133, 1177, 1199, 1243, 1331, 1397, 1441, 1507, 1529, 1573, 1639, 1661, 1727, 1793, 1837, 1859, 1903, 1969, 1991, 2057, 2101, 2123, 2167, 2189, 2299, 2321

Offset: 1

Author

Robert G. Wilson v, Jun 15 2003

Keywords

• nonn
• easy

Comments

Fifth row of A083140.

Integers k such that gcd(11*k, 210) = 1.

Examples

			a(2) = 11*11, a(3) = 11*13.
		

Links

• Amiram Eldar, Table of n, a(n) for n = 1..10000
• 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, 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).

Crossrefs

Cf. A084967 (5), A084968 (7), A084970 (13), A332799 (17), A332798 (19), A332797 (23), A008364 (11-rough numbers).

Cf. A008364, A038110, A038111, A083140.

Programs

Mathematica

11Select[ Range[210], GCD[ #, 2*3*5*7] == 1 & ]
Select[11*Range[0,200],GCD[#,210]==1&] (* Harvey P. Dale, Dec 23 2013 *)

PARI

is(n)=gcd(n,2310)==11 \\ Charles R Greathouse IV, Nov 19 2014

Formula

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

a(n) = a(n-48) + 2310 = a(n-1) + a(n-48) - a(n-49). - Charles R Greathouse IV, Nov 19 2014

Lim_{n->infinity} a(n)/n = A038111(5)/A038110(5) = 385/8 = 48.125. - Vladimir Shevelev, Jan 20 2015

a(n) = 11*A008364(n).

Extensions

a(47)-a(49) from Georg Fischer, Nov 07 2019

New name from Frank Ellermann, Feb 25 2020