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A222112
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Initial step in Goodstein sequences: write n-1 in hereditary binary representation, then bump to base 3.
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8
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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
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listen;
history;
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OFFSET
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1,3
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COMMENTS
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See A056004 for an alternate version.
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REFERENCES
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Helmut Schwichtenberg and Stanley S. Wainer, Proofs and Computations, Cambridge University Press, 2012; 4.4.1, page 148ff.
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LINKS
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EXAMPLE
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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.
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PROG
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(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
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CROSSREFS
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KEYWORD
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nonn
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AUTHOR
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STATUS
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approved
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