|
%I #17 Mar 07 2024 17:27:38
%S 1,4,9,10,13,18,19,22,27,28,31,36,37,40,45,46,49,54,55,58,63,64,67,72,
%T 73,76,81,82,85,90,91,94,99,100,103,108,109,112,117,118,121,126,127,
%U 130,135,136,139,144,145,148,153,154,157,162,163,166,171,172,175,180
%N Iterated sum of digits of n is a square.
%H <a href="/index/Rec#order_04">Index entries for linear recurrences with constant coefficients</a>, signature (1,0,1,-1).
%F a(n) = a(n-3)+9. If n is a multiple of 3 then a(n) = 3n, otherwise a(n) = 3n-2. Numbers of form {0, 1, 4} modulo 9 - _Henry Bottomley_, Jun 30 2000
%F a(1)=1, a(2)=4, a(3)=9, a(4)=10, a(n)=a(n-1)+a(n-3)-a(n-4). - _Harvey P. Dale_, Jan 26 2015
%F G.f.: x*(1+3*x+5*x^2) / ( (1+x+x^2)*(x-1)^2 ). - _R. J. Mathar_, Sep 22 2016
%F E.g.f.: (exp(x)*(9*x - 4) + 4*exp(-x/2)*cos(sqrt(3)*x/2))/3. - _Stefano Spezia_, Mar 07 2024
%e E.g. 58 -> 5+8 = 13 -> 1+3 = 4 is a square.
%t LinearRecurrence[{1,0,1,-1},{1,4,9,10},60] (* _Harvey P. Dale_, Jan 26 2015 *)
%Y Cf. A010888, A028839, A028845.
%K nonn,base,easy
%O 1,2
%A _N. J. A. Sloane_
%E More terms from _Patrick De Geest_, Jun 15 1999
|
