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 A222117 Goodstein sequence starting with 15. 25
 15, 111, 1283, 18752, 326593, 6588344, 150994943, 3524450280, 100077777775, 3138578427934, 106993479003783, 3937376861542204, 155568096352467863, 6568408356994335930, 295147905181357143919, 14063084452070776884879, 708235345355342213988445 (list; graph; refs; listen; history; text; internal format)
 OFFSET 0,1 COMMENTS To calculate a(n+1), write a(n) in the hereditary representation base n+2, then bump the base to n+3, then subtract 1; Compare to A222113: the underlying variants to define Goodstein sequences are equivalent. LINKS Nicholas Matteo, Table of n, a(n) for n = 0..383 (first 249 terms from Reinhard Zumkeller) R. L. Goodstein, On the Restricted Ordinal Theorem, The Journal of Symbolic Logic, Vol. 9, No. 2, Jun., 1944 Eric Weisstein's World of Mathematics, Goodstein Sequence Wikipedia, Goodstein's Theorem Reinhard Zumkeller, Haskell programs for Goodstein sequences EXAMPLE The first terms are: a(0) = 2^(2+1) + 2^2 + 2^1 + 2^0 = 15; a(1) = 3^(3+1) + 3^3 + 3^1 + 3^0 - 1 = 111; a(2) = 4^(4+1) + 4^4 + 4^1 - 1 = 4^(4+1) + 4^4 + 3*4^0 = 1283; a(3) = 5^(5+1) + 5^5 + 3*5^0 - 1 = 5^(5+1) + 5^5 + 2*5^0 = 18752; a(4) = 6^(6+1) + 6^6 + 2*6^0 - 1 = 6^(6+1) + 6^6 + 1 = 326593; a(5) = 7^(7+1) + 7^7 + 1 - 1 = 6588344; a(6) = 8^(8+1) + 8^8 - 1 = 150994943. PROG (Haskell)  see Link (PARI) lista(nn) = {print1(a = 15, ", "); for (n=2, nn, pd = Pol(digits(a, n)); q = sum(k=0, poldegree(pd), if (c=polcoeff(pd, k), c*x^subst(Pol(digits(k, n)), x, n+1), 0)); a = subst(q, x, n+1) - 1; print1(a, ", "); ); } \\ Michel Marcus, Feb 24 2016 CROSSREFS Cf. A215409 (start=3), A056193 (start=4), A059933 (start=16), A211378 (start=19). Sequence in context: A254869 A034184 A092646 * A105051 A105040 A298123 Adjacent sequences:  A222114 A222115 A222116 * A222118 A222119 A222120 KEYWORD nonn,fini AUTHOR Reinhard Zumkeller, Feb 13 2013 EXTENSIONS Offset changed to 0 by Nicholas Matteo, Aug 21 2019 STATUS approved

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Last modified September 20 11:01 EDT 2020. Contains 337264 sequences. (Running on oeis4.)