cp's OEIS Frontend

A273669 Decimal representation ends with either 2 or 9.

%I A273669 #28 Apr 15 2023 04:20:47
%S A273669 2,9,12,19,22,29,32,39,42,49,52,59,62,69,72,79,82,89,92,99,102,109,
%T A273669 112,119,122,129,132,139,142,149,152,159,162,169,172,179,182,189,192,
%U A273669 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
%N A273669 Decimal representation ends with either 2 or 9.
%C A273669 Natural numbers not in A273664.
%H A273669 Antti Karttunen, <a href="/A273669/b273669.txt">Table of n, a(n) for n = 1..10000</a>
%H A273669 <a href="/index/Rec#order_03">Index entries for linear recurrences with constant coefficients</a>, signature(1,1,-1).
%F A273669 a(n) = 10*(((n-2)+A000035(n))/2) + 2 [when n is odd], or + 9 [when n is even].
%F A273669 For n >= 5, a(n) = 2*a(n-2) - a(n-4).
%F A273669 a(n) = A126760(A084967(n)).
%F A273669 a(n) = A249746((3*A249745(n))-1).
%F A273669 Other identities. For all n >= 1:
%F A273669 A084967(n) = 5*A007310(n) = A007310(a(n)).
%F A273669 G.f.: x*(x^2+7*x+2)/((x+1)*(x-1)^2).
%F A273669 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
%t A273669 Select[Range@ 340, MemberQ[{2, 9}, Mod[#, 10]] &] (* or *)
%t A273669 Table[{10 n + 2, 10 n + 9}, {n, 0, 33}] // Flatten (* or *)
%t A273669 CoefficientList[Series[(-5/(1 - x) + (11 - x)/(-1 + x)^2 - 2/(1 + x))/2, {x, 0, 67}], x] (* _Michael De Vlieger_, Aug 07 2016 *)
%o A273669 (Scheme)
%o A273669 (define (A273669 n) (+ (* 10 (/ (+ (- n 2) (if (odd? n) 1 0)) 2)) (if (odd? n) 2 9)))
%Y A273669 Sequences A017293 and A017377 interleaved.
%Y A273669 Cf. A000035, A001622, A007310, A084967, A126760, A249745, A249746.
%Y A273669 Cf. also A273664, A249824, A275716.
%K A273669 nonn,base,easy
%O A273669 1,1
%A A273669 _Antti Karttunen_, Aug 06 2016