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

1,2

Comments

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

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).

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)

Example

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

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 *)

Prog

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

Crossrefs

Cf. A008592, A010692.

Sequence in context: A222947 A107226 A252663 * A259045 A029611 A053357

Adjacent sequences: A317630 A317631 A317632 * A317634 A317635 A317636

Keyword

nonn,easy

Author

Paul Curtz, Aug 02 2018

Extensions

Definition from Jianing Song, Aug 02 2018

Status

approved