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 A059934 #20 Feb 16 2025 08:32:44 %S A059934 0,2,60,467,3125,3127,6310,9842,15625,15627,15685,16092,18750,18752, %T A059934 53793641718868912174424175024032593379100060 %N A059934 Third step in Goodstein sequences, i.e., g(5) if g(2)=n: write g(4)=A057650(n) in hereditary representation base 4, bump to base 5, then subtract 1 to produce g(5). %C A059934 1.911...*10^2184 = a(18) < a(19) < ... < a(31) = a(18) + 18752. - _Pontus von Brömssen_, Sep 20 2020 %H A059934 Pontus von Brömssen, <a href="/A059934/b059934.txt">Table of n, a(n) for n = 2..17</a> %H A059934 R. L. Goodstein, <a href="http://www.jstor.org/stable/2268019">On the Restricted Ordinal Theorem</a>, J. Symb. Logic 9, 33-41, 1944. %H A059934 Eric Weisstein's World of Mathematics, <a href="https://mathworld.wolfram.com/GoodsteinSequence.html">Goodstein Sequence</a> %H A059934 Wikipedia, <a href="http://en.wikipedia.org/wiki/Goodstein's_theorem">Goodstein's Theorem</a> %H A059934 Reinhard Zumkeller, <a href="/A211378/a211378.hs.txt">Haskell programs for Goodstein sequences</a> %e A059934 a(12) = 15685 since with g(2) = 12 = 2^(2 + 1) + 2^2, we get g(3) = 3^(3 + 1) + 3^3-1 = 107 = 3^(3 + 1) + 2*3^2 + 2*3 + 2, g(4) = 4^(4 + 1) + 2*4^2 + 2*4 + 2-1 = 1065 and g(5) = 5^(5 + 1) + 2*5^2 + 2*5^1 + 1-1. %o A059934 (Haskell) -- See Link %o A059934 (Python) %o A059934 from sympy.ntheory.factor_ import digits %o A059934 def bump(n,b): %o A059934 s=digits(n,b)[1:] %o A059934 l=len(s) %o A059934 return sum(s[i]*(b+1)**bump(l-i-1,b) for i in range(l) if s[i]) %o A059934 def A059934(n): %o A059934 for i in range(2,5): %o A059934 n=bump(n,i)-1 %o A059934 return n # _Pontus von Brömssen_, Sep 20 2020 %Y A059934 Cf. A056004, A057650, A059933, A059935, A059936. %K A059934 nonn %O A059934 2,2 %A A059934 _Henry Bottomley_, Feb 12 2001