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 A191762 #19 Aug 11 2015 09:56:32 %S A191762 4,7,9,1,1,9,7,4,9,4,7,9,1,1,9,7,4,9,4,7,9,1,1,9,7,4,9,4,7,9,1,1,9,7, %T A191762 4,9,4,7,9,1,1,9,7,4,9,4,7,9,1,1,9,7,4,9,4,7,9,1,1,9,7,4,9 %N A191762 Digital roots of the nonzero even squares. %C A191762 Period 9: repeat [4, 7, 9, 1, 1, 9, 7, 4, 9]. Bisection of A056992. %C A191762 The digits in the 9-cycle of this sequence are the same as the digits in the 9-cycle of the digital roots of the odd squares A191760(n). However, these are offset differently (by the first five terms) and hence constitute a different sequence. %H A191762 <a href="/index/Rec#order_09">Index entries for linear recurrences with constant coefficients</a>, signature (0,0,0,0,0,0,0,0,1). %F A191762 a(n) = 3*(1 + cos(2*n*Pi/3) + cos(4*n*Pi/3)) + (4*n^4 + 7*n^6 + 2*n^8) mod 9. %F A191762 G.f.: x*(4 + 7*x + 9*x^2 + x^3 + x^4 + 9*x^5 + 7*x^6 + 4*x^7 + 9*x^8)/(1-x^9) (note that the coefficients of x in the numerator are precisely the terms that constitute the periodic cycle of the sequence). %F A191762 a(n) = A010888(A016742(n)). - _Michel Marcus_, Aug 11 2015 %e A191762 The fifth even, nonzero square is 100, which has digital root 1. Hence a(5)=1. %t A191762 DigitalRoot[n_Integer?Positive]:=FixedPoint[Plus@@IntegerDigits[#]&,n];DigitalRoot[(2#)^2] &/@Range[63] %o A191762 (PARI) a(n)=(4*n^2-1)%9+1 \\ _Charles R Greathouse IV_, Jun 19 2011 %Y A191762 Cf. A010888, A016742, A191760, A191761. %K A191762 nonn,base,easy %O A191762 1,1 %A A191762 _Ant King_, Jun 18 2011