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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
 16, 112, 1284, 18753, 326594, 6588345, 150994944, 3524450281, 100077777776, 3138578427935, 106993479003784, 3937376861542205, 155568096352467864, 6568408356994335931, 295147905181357143920, 14063084452070776884880, 708235345355342213988446 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,1 COMMENTS Compare to A222117: the underlying variants to define Goodstein sequences are equivalent. REFERENCES Helmut Schwichtenberg and Stanley S. Wainer, Proofs and Computations, Cambridge University Press, 2012; 4.4.1, page 148ff. LINKS Reinhard Zumkeller, Table of n, a(n) for n = 1..250 R. L. Goodstein, On the Restricted Ordinal Theorem, The Journal of Symbolic Logic, Vol. 9, No. 2, Jun., 1944. Wikipedia, Goodstein's Theorem Reinhard Zumkeller, Haskell programs for Goodstein sequences EXAMPLE a(1) - 1 = 15 = 2^3 + 2^2 + 2^1 + 2^0 = 2^(2^1+1) + 2^2 + 2^1 + 2^0 -> a(2) = 3^(3^1+1) + 3^3 + 3^1 + 3^0 = 112; a(2) - 1 = 111 = 3^(3^1+1) + 3^3 + 3^1 -> a(3) = 4^(4^1+1) + 4^4 + 4^1 = 1284; a(3) - 1 = 1283 = 4^(4^1+1) + 4^4 + 3*4^0 -> a(4) = 5^(5^1+1) + 5^5 + 3*5^0 = 18753; a(4) - 1 = 18752 = 5^(5^1+1) + 5^5 + 2*5^0 -> a(5) = 6^(6^1+1) + 6^6 + 2*6^0 = 326594; a(5) - 1 = 326593 = 6^(6^1+1) + 6^6 + 6^0 -> a(6)  = 7^(7^1+1) + 7^7 + 7^0 = 6588345. PROG (Haskell)  see Link CROSSREFS Cf. A222112. Sequence in context: A000143 A258546 A205964 * A229531 A253460 A081194 Adjacent sequences:  A222110 A222111 A222112 * A222114 A222115 A222116 KEYWORD nonn,fini AUTHOR Reinhard Zumkeller, Feb 13 2013 STATUS approved

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Last modified January 21 10:59 EST 2020. Contains 331105 sequences. (Running on oeis4.)