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A130877 Numbers that are congruent to {0, 5} mod 9.

%I A130877 #75 Apr 12 2025 16:39:32
%S A130877 0,5,9,14,18,23,27,32,36,41,45,50,54,59,63,68,72,77,81,86,90,95,99,
%T A130877 104,108,113,117,122,126,131,135,140,144,149,153,158,162,167,171,176,
%U A130877 180,185,189,194,198,203,207,212,216,221,225,230,234,239,243,248,252,257
%N A130877 Numbers that are congruent to {0, 5} mod 9.
%C A130877 Numbers m such that m = digitsum(k*(m+k)) for some k>=0.
%C A130877 The first differences are 2-periodic: 5, 4, 5, 4, etc. The minimum numbers k associated to the first elements of the sequence are (m,k): (0,0), (5,2), (9,3), (14,5), (18,15), (23,44), (27,42), (32,119), etc.
%H A130877 <a href="/index/Rec#order_03">Index entries for linear recurrences with constant coefficients</a>, signature (1,1,-1).
%F A130877 a(n) = a(n-2) + 9 for n >= 3.
%F A130877 a(n) = 9/2*(n+1) - 4 + Sum{j=0..n} (-1)^j/2.
%F A130877 O.g.f.: x^2(5+4x)/((1+x)(1-x)^2). a(n) = 9(n-1)/2+(1+(-1)^n)/4. - _R. J. Mathar_, Jun 13 2008
%F A130877 a(n+1) = Sum_{k>=0} A030308(n,k)*A116453(k+1). - _Philippe Deléham_, Oct 17 2011
%F A130877 a(n) = 5n - 5 - floor((n-1)/2). - _Wesley Ivan Hurt_, Oct 25 2013
%F A130877 a(n) = ceiling(9*(n-1)/2). - _Alois P. Heinz_, Apr 12 2025
%p A130877 op(select(n->n mod 9=0 or n mod 9=5,[$0..257])); # _Paolo P. Lava_, Jul 12 2018
%p A130877 # second Maple program:
%p A130877 a:= n-> ceil(9*(n-1)/2):
%p A130877 seq(a(n), n=1..58);  # _Alois P. Heinz_, Apr 12 2025
%t A130877 Table[5n-5-Floor[(n-1)/2], {n,100}] (* _Wesley Ivan Hurt_, Oct 25 2013 *)
%t A130877 Select[Range[0,300],MemberQ[{0,5},Mod[#,9]]&] (* or *) LinearRecurrence[ {1,1,-1},{0,5,9},60] (* _Harvey P. Dale_, Aug 04 2019 *)
%o A130877 (PARI) forstep(n=0,200,[5,4],print1(n", ")) \\ _Charles R Greathouse IV_, Oct 17 2011
%Y A130877 Cf. A008591, A017221.
%K A130877 nonn,easy
%O A130877 1,2
%A A130877 _Paolo P. Lava_ and _Giorgio Balzarotti_, Jul 25 2007