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

1,1

Comments

Fifth row of A083140.

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

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).

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).

Example

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

Mathematica

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

Prog

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

Crossrefs

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

Cf. A008364, A038110, A038111, A083140.

Sequence in context: A089707 A223391 A337707 * A045592 A045595 A228440

Adjacent sequences: A084966 A084967 A084968 * A084970 A084971 A084972

Keyword

nonn,easy

Author

Robert G. Wilson v, Jun 15 2003

Extensions

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

New name from Frank Ellermann, Feb 25 2020

Status

approved