This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.
%I A010690 #53 Jun 09 2025 09:02:31
%S A010690 1,9,1,9,1,9,1,9,1,9,1,9,1,9,1,9,1,9,1,9,1,9,1,9,1,9,1,9,1,9,1,9,1,9,
%T A010690 1,9,1,9,1,9,1,9,1,9,1,9,1,9,1,9,1,9,1,9,1,9,1,9,1,9,1,9,1,9,1,9,1,9,
%U A010690 1,9,1,9,1,9,1,9,1,9,1,9,1
%N A010690 Period 2: repeat (1,9).
%C A010690 Digital roots of the nonzero square triangular numbers. - _Ant King_, Jan 21 2012
%C A010690 Continued fraction expansion of A176019. - _R. J. Mathar_, Mar 08 2012
%C A010690 Exp( Sum_{n >= 1} a(n-1)*x^n/n ) = 1 + x + 5*x^2 + 5*x^3 + 15*x^4 + 15*x^5 + ... is the o.g.f. for A189976 (taken with an offset of 0). - _Peter Bala_, Mar 13 2015
%C A010690 Final digit of 9^n. - _Martin Renner_, Jun 11 2020
%C A010690 Decimal expansion of 19/99. - _Stefano Spezia_, Feb 09 2025
%H A010690 <a href="/index/Rec#order_02">Index entries for linear recurrences with constant coefficients</a>, signature (0,1).
%F A010690 G.f.: (1+9x)/((1-x)(1+x)). - _R. J. Mathar_, Nov 21 2011
%F A010690 a(n) = 9^n mod 10. - _Martin Renner_, Jun 11 2020
%F A010690 E.g.f.: cosh(x) + 9*sinh(x). - _Stefano Spezia_, Feb 09 2025
%F A010690 From _Amiram Eldar_, Jun 09 2025: (Start)
%F A010690 With offset 1:
%F A010690 Multiplicative with a(2^e) = 9, a(p^e) = 1 for an odd prime p.
%F A010690 Dirichlet g.f.: zeta(s) * (1 + 1/2^(s-3)). (End)
%e A010690 0.191919191919191919191919191919191919191...
%t A010690 5+4*(-1)^# &/@Range[81] (* _Ant King_, Jan 21 2012 *)
%o A010690 (PARI) a(n)=1; if(n%2==1, 9, 1) \\ _Felix Fröhlich_, Aug 11 2014
%Y A010690 Cf. A008592, A001019 (9^n), A014393, A189976.
%K A010690 nonn,cons,easy
%O A010690 0,2
%A A010690 _N. J. A. Sloane_