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 A117618 #39 Feb 16 2025 08:33:00 %S A117618 1,6,7,10,22,683 %N A117618 Least number with complexity height of n, under integer complexity A005245. %C A117618 Consider the recursion: A005245(n), A005245(A005245(n)), A005245(A005245(A005245(n))), ... which we know is finite before reaching a fixed point, as A005245(n) <= n. The number of steps needed to reach such a fixed point is the complexity height of n (with respect to the A005245 measure of complexity, there being others in the OEIS). %C A117618 a(7) >= 872573642639 = A005520(89). - _David A. Corneth_, May 06 2024 %D A117618 W. A. Beyer, M. L. Stein and S. M. Ulam, The Notion of Complexity. Report LA-4822, Los Alamos Scientific Laboratory of the University of California, Los Alamos, NM, December 1971. %D A117618 R. K. Guy, Unsolved Problems in Number Theory, Sect. F26. %H A117618 W. A. Beyer, M. L. Stein and S. M. Ulam, <a href="/A003037/a003037.pdf">The Notion of Complexity</a>. Report LA-4822, Los Alamos Scientific Laboratory of the University of California, Los Alamos, NM, December 1971. [Annotated scanned copy] %H A117618 R. K. Guy, <a href="http://www.jstor.org/stable/2323338">Some suspiciously simple sequences</a>, Amer. Math. Monthly 93 (1986), 186-190; 94 (1987), 965; 96 (1989), 905. %H A117618 E. Pegg, Jr., <a href="http://library.wolfram.com/infocenter/MathSource/5175/">Integer Complexity.</a> %H A117618 Eric Weisstein's World of Mathematics, <a href="https://mathworld.wolfram.com/IntegerComplexity.html">Integer Complexity.</a> %H A117618 <a href="/index/Com#complexity">Index to sequences related to the complexity of n</a> %F A117618 a(n) = least k such that A005245^(n)(k) = A005245^(n-1)(k) but (if n>1) A005245^(n-1)(k) != A005245^(n-2)(k), where ^ denotes repeated application. %F A117618 For n >= 3, a(n) = A005520(a(n-1)). - _Max Alekseyev_, May 06 2024 %e A117618 a(1) = 1 because the A005245 complexity of 1 is 1, already giving a fixed point. %e A117618 a(2) = 6 because it is the smallest x such that A005245(x) =/= x and A005245(x) = A005245(A005245(x)). %e A117618 a(3) = 7 because 7 is the least number x with complexity 6, thus taking a further step of recursion to reach a fixed point. %e A117618 a(4) = 10 because 10 is the least number with complexity 7. %e A117618 a(5) = 22 because 22 is the least number with complexity 10. %e A117618 a(6) = 683 because 683 is the least number with complexity 22. %e A117618 a(7) = the least number with complexity 683. %Y A117618 Cf. A003037, A003313, A005245, A005421, A005520, A025280, A061373, A064097, A076091, A076142. %K A117618 nonn,more,hard %O A117618 1,2 %A A117618 _Jonathan Vos Post_, Apr 07 2006 %E A117618 a(2)=6 inserted by _Giovanni Resta_, Jun 15 2016 %E A117618 Edited by _Max Alekseyev_, May 06 2024