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A222112
Initial step in Goodstein sequences: write n-1 in hereditary binary representation, then bump to base 3.
8
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
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
R. L. Goodstein, On the Restricted Ordinal Theorem, The Journal of Symbolic Logic, Vol. 9, No. 2, Jun., 1944.
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
KEYWORD
nonn
AUTHOR
Reinhard Zumkeller, Feb 13 2013
STATUS
approved