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 A114469 #49 Aug 01 2025 00:15:57
%S A114469 1,3,21,209,2090,20899,208988,2089877,20898765,208987641,2089876403,
%T A114469 20898764025,208987640250,2089876402500,20898764024998,
%U A114469 208987640249979,2089876402499788,20898764024997874,208987640249978734,2089876402499787338,20898764024997873377,208987640249978733770,2089876402499787337693,20898764024997873376928,208987640249978733769273,2089876402499787337692721
%N A114469 Number of decimal digits in Lucas(10^n).
%C A114469 From _Hans J. H. Tuenter_, Jul 15 2025: (Start)
%C A114469 This sequence can be constructed by taking the first n digits of the decimal expansion of log_10(phi) = A097348 and adding 1. For example,
%C A114469 a(0) = 1,
%C A114469 a(1) = 2+1 = 3,
%C A114469 a(2) = 20+1 = 21,
%C A114469 a(3) = 208+1 = 209,
%C A114469 a(4) = 2089+1 = 2090,
%C A114469 a(5) = 20898+1 = 20899.
%C A114469 Alternatively, a(n)-1 is the first n digits of A097348. (End)
%C A114469 The individual digits of log_10(phi), and thus sequence A097348, can be extracted using d(n) = a(n)-10*a(n-1)+9. - _Hans J. H. Tuenter_, Jul 25 2025
%H A114469 Hans J. H. Tuenter, <a href="/A114469/b114469.txt">Table of n, a(n) for n = 0..100</a>
%H A114469 Eric Weisstein's World of Mathematics, <a href="https://mathworld.wolfram.com/LucasNumber.html">Lucas Number</a>.
%F A114469 Limit_{n->oo} a(n)/10^n = A097348. - _Amiram Eldar_, Apr 14 2022
%F A114469 a(n) = 1+floor(10^n*log_10(phi)), where phi = (1+sqrt(5))/2, the golden ratio. - _Hans J. H. Tuenter_, Jul 13 2025.
%F A114469 From _Hans J. H. Tuenter_, Jul 25 2025: (Start)
%F A114469 a(n) = 1 + Sum_{i=0..n} d(i)*10^(n-i),
%F A114469 a(n) = 10*a(n-1)-9+d(n),
%F A114469 where d(i) = A097348(i-1) is the coefficient of 10^(-i) in the decimal expansion of log_10(phi). (End)
%t A114469 Table[IntegerLength[LucasL[10^n]], {n, 0, 7}] (* _Jean-François Alcover_, Jan 24 2018 *)
%Y A114469 Cf. A068070. - _R. J. Mathar_, Dec 13 2008
%Y A114469 Cf. A000032, A001622, A055642, A097348.
%K A114469 nonn,base
%O A114469 0,2
%A A114469 _Eric W. Weisstein_, Nov 30 2005
%E A114469 a(8)-a(10) from _Amiram Eldar_, Apr 14 2022
%E A114469 a(11)-a(25) from _Hans J. H. Tuenter_, Jul 15 2025