A317633 Numbers congruent to {1, 7, 9} mod 10.

1, 7, 9, 11, 17, 19, 21, 27, 29, 31, 37, 39, 41, 47, 49, 51, 57, 59, 61, 67, 69, 71, 77, 79, 81, 87, 89, 91, 97, 99, 101, 107, 109, 111, 117, 119, 121, 127, 129, 131, 137, 139, 141, 147, 149, 151, 157, 159, 161, 167, 169

Offset: 1

Author

Paul Curtz, Aug 02 2018

Keywords

• nonn
• easy

Comments

When multiplied by 10, one gets the numbers ending in "dix" in French (10, 70, 90, 110, ...).

Examples

			G.f. = x + 7*x^2 + 9*x^3+ 11*x^4 + 17*x^5 + 19*x^6 + 21*x^7 + 27*x^8 + ... - _Michael Somos_, Aug 19 2018
		

Links

• G. C. Greubel, Table of n, a(n) for n = 1..5000
• Index entries for linear recurrences with constant coefficients, signature (1,0,1,-1).

Crossrefs

Cf. A008592, A010692.

Programs

Magma

[n: n in [0..170]|n mod 10 in {1, 7, 9}]; // Vincenzo Librandi, Aug 05 2018

Mathematica

Table[2 n + 4 Floor[(n + 1)/3] - 1, {n, 1, 60}] (* Bruno Berselli, Jul 02 2018 *)
Select[Range[0, 250], MemberQ[{1, 7, 9}, Mod[#, 10]]&] (* Vincenzo Librandi, Aug 05 2018 *)
CoefficientList[ Series[(x^3 + 2x^2 + 6x + 1)/((x - 1)^2 (x^2 + x + 1)), {x, 0, 60}], x] (* or *)
LinearRecurrence[{1, 0, 1, -1}, {1, 7, 9, 11}, 61] (* Robert G. Wilson v, Aug 08 2018 *)

PARI

x='x+O('x^60); Vec(x*(1+6*x+2*x^2+x^3)/((1-x)^2*(1+x+x^2))) \\ G. C. Greubel, Aug 08 2018

Formula

a(n) = a(n-3) + 10, a(1) = 1, a(2) = 7, a(3) = 9.

From Bruno Berselli, Jul 02 2018: (Start)

G.f.: x*(1 + 6*x + 2*x^2 + x^3)/((1 - x)^2*(1 + x + x^2)).

a(n) = 2*n + 4*floor((n+1)/3) - 1. (End)

Extensions

Definition from Jianing Song, Aug 02 2018