login
The OEIS Foundation is supported by donations from users of the OEIS and by a grant from the Simons Foundation.

 

Logo


Hints
(Greetings from The On-Line Encyclopedia of Integer Sequences!)
A222112 Initial step in Goodstein sequences: write n-1 in hereditary binary representation, then bump to base 3. 7

%I

%S 0,1,3,4,27,28,30,31,81,82,84,85,108,109,111,112,7625597484987,

%T 7625597484988,7625597484990,7625597484991,7625597485014,

%U 7625597485015,7625597485017,7625597485018,7625597485068,7625597485069,7625597485071,7625597485072,7625597485095

%N Initial step in Goodstein sequences: write n-1 in hereditary binary representation, then bump to base 3.

%C See A056004 for an alternate version.

%D Helmut Schwichtenberg and Stanley S. Wainer, Proofs and Computations, Cambridge University Press, 2012; 4.4.1, page 148ff.

%H Reinhard Zumkeller, <a href="/A222112/b222112.txt">Table of n, a(n) for n = 1..10000</a>

%H R. L. Goodstein, <a href="http://www.jstor.org/stable/2268019">On the Restricted Ordinal Theorem</a>, The Journal of Symbolic Logic, Vol. 9, No. 2, Jun., 1944.

%H Wikipedia, <a href="http://en.wikipedia.org/wiki/Goodstein&#39;s_theorem">Goodstein's Theorem</a>

%H Reinhard Zumkeller, <a href="/A211378/a211378.hs.txt">Haskell programs for Goodstein sequences</a>

%e n = 19: 19 - 1 = 18 = 2^4 + 2^1 = 2^2^2 + 2^1

%e -> a(19) = 3^3^3 + 3^1 = 7625597484990;

%e n = 20: 20 - 1 = 19 = 2^4 + 2^1 + 2^0 = 2^2^2 + 2^1 + 2^0

%e -> a(20) = 3^3^3 + 3^1 + 3^0 = 7625597484991;

%e n = 21: 21 - 1 = 20 = 2^4 + 2^2 = 2^2^2 + 2^2

%e -> a(21) = 3^3^3 + 3^3 = 7625597485014.

%o (Haskell) see Link

%o (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

%Y Cf. A056004: G_1(n), A057650 G_2(n), A056041; A266201: G_n(n);

%Y 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).

%K nonn

%O 1,3

%A _Reinhard Zumkeller_, Feb 13 2013

Lookup | Welcome | Wiki | Register | Music | Plot 2 | Demos | Index | Browse | More | WebCam
Contribute new seq. or comment | Format | Style Sheet | Transforms | Superseeker | Recent
The OEIS Community | Maintained by The OEIS Foundation Inc.

License Agreements, Terms of Use, Privacy Policy. .

Last modified February 21 20:42 EST 2020. Contains 332111 sequences. (Running on oeis4.)