A084970 Numbers whose smallest prime factor is 13.

13, 169, 221, 247, 299, 377, 403, 481, 533, 559, 611, 689, 767, 793, 871, 923, 949, 1027, 1079, 1157, 1261, 1313, 1339, 1391, 1417, 1469, 1651, 1703, 1781, 1807, 1937, 1963, 2041, 2119, 2171, 2197, 2249, 2327, 2353, 2483, 2509, 2561, 2587, 2743, 2873

Offset: 1

Author

Robert G. Wilson v, Jun 15 2003

Keywords

• nonn
• easy

Examples

			a(2) = 13*13, a(3) = 13*17.
		

Links

• Amiram Eldar, Table of n, a(n) for n = 1..10000
• Index entries for linear recurrences with constant coefficients, order 481.

Crossrefs

Sixth row of A083140.

Cf. A084967 (5), A084968 (7), A084969 (11), A332799 (17), A332798 (19), A332797 (23), A008365 (13-rough numbers).

Programs

Mathematica

Select[ 13Range@ 225, GCD[#, 2310] == 1 &] (* Robert G. Wilson v, Dec 18 2014 *)

PARI

is(n)=n%13==0 && gcd(n,2310)==1 \\ Charles R Greathouse IV, Nov 19 2014

Formula

a(n) = a(n-480) + 30030 = a(n-1) + a(n-480) - a(n-481). - Charles R Greathouse IV, Nov 19 2014

Lim_{n->infinity} a(n)/n = A038111(6)/A038110(6) = 1001/16 = 62.5625. - Vladimir Shevelev, Jan 20 2015

a(n) = 13*A008365(n).

Extensions

More terms from David Wasserman, Oct 19 2004