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 A222112 Initial step in Goodstein sequences: write n-1 in hereditary binary representation, then bump to base 3. 7
 0, 1, 3, 4, 27, 28, 30, 31, 81, 82, 84, 85, 108, 109, 111, 112, 7625597484987, 7625597484988, 7625597484990, 7625597484991, 7625597485014, 7625597485015, 7625597485017, 7625597485018, 7625597485068, 7625597485069, 7625597485071, 7625597485072, 7625597485095 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,3 COMMENTS See A056004 for an alternate version. 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..10000 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 n = 19: 19 - 1 = 18 = 2^4 + 2^1 = 2^2^2 + 2^1 -> a(19) = 3^3^3 + 3^1 = 7625597484990; n = 20: 20 - 1 = 19 = 2^4 + 2^1 + 2^0 = 2^2^2 + 2^1 + 2^0 -> a(20) = 3^3^3 + 3^1 + 3^0 = 7625597484991; n = 21: 21 - 1 = 20 = 2^4 + 2^2 = 2^2^2 + 2^2 -> a(21) = 3^3^3 + 3^3 = 7625597485014. PROG (Haskell) see Link (PARI) A222112(n)=sum(i=1, #n=binary(n-1), if(n[i], 3^if(#n-i<2, #n-i, A222112(#n-i+1)))) \\ See A266201 for more general code. - M. F. Hasler, Feb 13 2017, edited Feb 19 2017 CROSSREFS Cf. A056004: G_1(n), A057650 G_2(n), A056041;  A266201: G_n(n); Cf. A215409: G_n(3), A056193: G_n(4), A266204: G_n(5), A266205: G_n(6), A222117: G_n(15), A059933: G_n(16), A211378: G_n(19). Sequence in context: A151372 A258103 A300373 * A032832 A041021 A041022 Adjacent sequences:  A222109 A222110 A222111 * A222113 A222114 A222115 KEYWORD nonn AUTHOR Reinhard Zumkeller, Feb 13 2013 STATUS approved

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Last modified January 21 10:26 EST 2020. Contains 331105 sequences. (Running on oeis4.)