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A222113 Goodstein sequence starting with a(1) = 16: to calculate a(n) for n>1, subtract 1 from a(n-1) and write the result in the hereditary representation base n, then bump the base to n+1. 4

%I

%S 16,112,1284,18753,326594,6588345,150994944,3524450281,100077777776,

%T 3138578427935,106993479003784,3937376861542205,155568096352467864,

%U 6568408356994335931,295147905181357143920,14063084452070776884880,708235345355342213988446

%N Goodstein sequence starting with a(1) = 16: to calculate a(n) for n>1, subtract 1 from a(n-1) and write the result in the hereditary representation base n, then bump the base to n+1.

%C Compare to A222117: the underlying variants to define Goodstein sequences are equivalent.

%D Helmut Schwichtenberg and Stanley S. Wainer, Proofs and Computations, Cambridge University Press, 2012; 4.4.1, page 148ff.

%H Reinhard Zumkeller, <a href="/A222113/b222113.txt">Table of n, a(n) for n = 1..250</a>

%H R. L. Goodstein, <a href="http://www.jstor.org/stable/2268019">On the Restricted Ordinal Theorem</a>, The Journal of Symbolic Logic, Vol. 9, No. 2, Jun., 1944.

%H Wikipedia, <a href="http://en.wikipedia.org/wiki/Goodstein&#39;s_theorem">Goodstein's Theorem</a>

%H Reinhard Zumkeller, <a href="/A211378/a211378.hs.txt">Haskell programs for Goodstein sequences</a>

%e a(1) - 1 = 15 = 2^3 + 2^2 + 2^1 + 2^0 = 2^(2^1+1) + 2^2 + 2^1 + 2^0

%e -> a(2) = 3^(3^1+1) + 3^3 + 3^1 + 3^0 = 112;

%e a(2) - 1 = 111 = 3^(3^1+1) + 3^3 + 3^1

%e -> a(3) = 4^(4^1+1) + 4^4 + 4^1 = 1284;

%e a(3) - 1 = 1283 = 4^(4^1+1) + 4^4 + 3*4^0

%e -> a(4) = 5^(5^1+1) + 5^5 + 3*5^0 = 18753;

%e a(4) - 1 = 18752 = 5^(5^1+1) + 5^5 + 2*5^0

%e -> a(5) = 6^(6^1+1) + 6^6 + 2*6^0 = 326594;

%e a(5) - 1 = 326593 = 6^(6^1+1) + 6^6 + 6^0

%e -> a(6) = 7^(7^1+1) + 7^7 + 7^0 = 6588345.

%o (Haskell) see Link

%Y Cf. A222112.

%K nonn,fini

%O 1,1

%A _Reinhard Zumkeller_, Feb 13 2013

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Last modified February 26 17:19 EST 2020. Contains 332293 sequences. (Running on oeis4.)