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 A100402 #78 Mar 20 2025 12:11:17
%S A100402 1,4,7,1,4,7,1,4,7,1,4,7,1,4,7,1,4,7,1,4,7,1,4,7,1,4,7,1,4,7,1,4,7,1,
%T A100402 4,7,1,4,7,1,4,7,1,4,7,1,4,7,1,4,7,1,4,7,1,4,7,1,4,7,1,4,7,1,4,7,1,4,
%U A100402 7,1,4,7,1,4,7,1,4,7,1,4,7,1,4,7,1,4,7,1,4,7,1,4,7,1,4,7,1,4,7,1,4,7,1,4,7
%N A100402 Digital root of 4^n.
%C A100402 Equals A141725 mod 9. - _Paul Curtz_, Sep 15 2008
%C A100402 Sequence is the digital root of A016777. - _Odimar Fabeny_, Sep 13 2010
%C A100402 Digital root of the powers of any number congruent to 4 mod 9. - _Alonso del Arte_, Jan 26 2014
%C A100402 Period 3: repeat [1, 4, 7]. - _Wesley Ivan Hurt_, Aug 26 2014
%C A100402 From _Timothy L. Tiffin_, Dec 02 2023: (Start)
%C A100402 The period 3 digits of this sequence are the same as those of A070403 (digital root of 7^n) but the order is different: [1, 4, 7] vs. [1, 7, 4].
%C A100402 The digits in this sequence appear in the decimal expansions of the following rational numbers: 49/333, 490/333, 4900/333, .... (End)
%D A100402 Cecil Balmond, Number 9: The Search for the Sigma Code. Munich, New York: Prestel (1998): 203.
%H A100402 <a href="/index/Rec#order_03">Index entries for linear recurrences with constant coefficients</a>, signature (0,0,1).
%F A100402 a(n) = 4^n mod 9. - _Zerinvary Lajos_, Nov 25 2009
%F A100402 From _R. J. Mathar_, Apr 13 2010: (Start)
%F A100402 a(n) = a(n-3) for n>2.
%F A100402 G.f.: (1+4*x+7*x^2)/ ((1-x)*(1+x+x^2)). (End)
%F A100402 a(n) = A010888(A000302(n)). - _Michel Marcus_, Aug 25 2014
%F A100402 a(n) = 3*A010872(n) + 1. - _Robert Israel_, Aug 25 2014
%F A100402 a(n) = 4 - 3*cos(2*n*Pi/3) - sqrt(3)*sin(2*n*Pi/3). - _Wesley Ivan Hurt_, Jun 30 2016
%F A100402 a(n) = A153130(2n). - _Timothy L. Tiffin_, Dec 01 2023
%F A100402 a(n) = A010888(A001022(n)) = A010888(A009966(n)) = A010888(A009975(n)) = A010888(A009984(n)) = A010888(A087752(n)) = A010888(A121013(n)). - _Timothy L. Tiffin_, Dec 02 2023
%F A100402 a(n) = A010888(4*a(n-1)). - _Stefano Spezia_, Mar 20 2025
%e A100402 4^2 = 16, digitalroot(16) = 7, the third entry.
%t A100402 Table[PowerMod[4, n, 9], {n, 0, 100}] (* _Timothy L. Tiffin_, Dec 03 2023 *)
%t A100402 StringRepeat["1, 4, 7, ", 100] (* _Timothy L. Tiffin_, Dec 03 2023 *)
%o A100402 (Sage) [power_mod(4, n, 9) for n in range(0, 105)] # _Zerinvary Lajos_, Nov 25 2009
%o A100402 (PARI) a(n)=[1,4,7][1+n%3]; \\ _Joerg Arndt_, Aug 26 2014
%Y A100402 Cf. Digital roots of powers of c mod 9: c = 2, A153130; c = 5, A070366; c = 7, A070403; c = 8, A010689.
%Y A100402 Cf. A000302, A001022, A009966, A009975, A009984, A010872, A010888, A070403, A087752, A121013, A141725, A016777.
%K A100402 easy,nonn,base
%O A100402 0,2
%A A100402 _Cino Hilliard_, Dec 31 2004