A273669 Decimal representation ends with either 2 or 9.

2, 9, 12, 19, 22, 29, 32, 39, 42, 49, 52, 59, 62, 69, 72, 79, 82, 89, 92, 99, 102, 109, 112, 119, 122, 129, 132, 139, 142, 149, 152, 159, 162, 169, 172, 179, 182, 189, 192, 199, 202, 209, 212, 219, 222, 229, 232, 239, 242, 249, 252, 259, 262, 269, 272, 279, 282, 289, 292, 299, 302, 309, 312, 319, 322, 329, 332, 339

Offset: 1

Author

Antti Karttunen, Aug 06 2016

Keywords

• nonn
• base
• easy

Comments

Natural numbers not in A273664.

Links

• Antti Karttunen, Table of n, a(n) for n = 1..10000
• Index entries for linear recurrences with constant coefficients, signature(1,1,-1).

Crossrefs

Sequences A017293 and A017377 interleaved.

Cf. A000035, A001622, A007310, A084967, A126760, A249745, A249746.

Cf. also A273664, A249824, A275716.

Programs

Mathematica

Select[Range@ 340, MemberQ[{2, 9}, Mod[#, 10]] &] (* or *)
Table[{10 n + 2, 10 n + 9}, {n, 0, 33}] // Flatten (* or *)
CoefficientList[Series[(-5/(1 - x) + (11 - x)/(-1 + x)^2 - 2/(1 + x))/2, {x, 0, 67}], x] (* Michael De Vlieger, Aug 07 2016 *)

Scheme

(define (A273669 n) (+ (* 10 (/ (+ (- n 2) (if (odd? n) 1 0)) 2)) (if (odd? n) 2 9)))

Formula

a(n) = 10*(((n-2)+A000035(n))/2) + 2 [when n is odd], or + 9 [when n is even].

For n >= 5, a(n) = 2*a(n-2) - a(n-4).

a(n) = A126760(A084967(n)).

a(n) = A249746((3*A249745(n))-1).

Other identities. For all n >= 1:

A084967(n) = 5*A007310(n) = A007310(a(n)).

G.f.: x*(x^2+7*x+2)/((x+1)*(x-1)^2).

Sum_{n>=1} (-1)^(n+1)/a(n) = sqrt((1+1/sqrt(5))/2)*phi^2*Pi/10 - log(phi)/(2*sqrt(5)) - log(2)/5, where phi is the golden ratio (A001622). - Amiram Eldar, Apr 15 2023