login
The OEIS is supported by the many generous donors to the OEIS Foundation.

 

Logo
Hints
(Greetings from The On-Line Encyclopedia of Integer Sequences!)
A271557 a(n) = G_n(10), where G is the Goodstein function defined in A266201. 11
10, 83, 1025, 15625, 279935, 4215754, 84073323, 1937434592, 50000555551, 1426559238830, 44580503598539, 1514375534972427, 55560034130686045, 2189469451908364943, 92233720368553350471, 4136201309431691363859, 196732040376482697880697, 9892098278301567958688175 (list; graph; refs; listen; history; text; internal format)
OFFSET
0,1
LINKS
R. L. Goodstein, On the Restricted Ordinal Theorem, The Journal of Symbolic Logic 9, no. 2 (1944), 33-41.
EXAMPLE
G_1(10) = B_2(10)-1 = B_2(2^(2+1)+2)-1 = 3^(3+1)+3-1 = 83;
G_2(10) = B_3(3^(3+1)+2)-1 = 4^(4+1)+2-1 = 1025;
G_3(10) = B_4(4^(4+1)+1)-1 = 5^(5+1)+1-1 = 15625;
G_4(10) = B_5(5*5^(5+1))-1 = 6^(6+1)-1= 279935;
G_5(10) = B_6(5*6^6+5*6^5+5*6^4+5*6^3+5*6^2+5*6+5)-1 = 5*7^7+5*7^5+5*7^4+5*7^3+5*7^2+5*7+5-1 = 4215754;
G_6(10) = B_7(5*7^7+5*7^5+5*7^4+5*7^3+5*7^2+5*7+4)-1 = 5*8^8+5*8^5+5*8^4+5*8^3+5*8^2+5*8+4-1 = 84073323;
G_7(10) = B_8(5*8^8+5*8^5+5*8^4+5*8^3+5*8^2+5*8+3)-1 = 5*9^9+5*9^5+5*9^4+5*9^3+5*9^2+5*9+3-1 = 1937434592;
G_8(10) = B_9(5*9^9+5*9^5+5*9^4+5*9^3+5*9^2+5*9+2)-1 = 5*10^10+5*10^5+5*10^4+5*10^3+5*10^2+5*10+2-1 = 50000555551.
PROG
(PARI) lista(nn) = {print1(a = 10, ", "); 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, ", "); ); }
CROSSREFS
Cf. A056193: G_n(4), A059933: G_n(16), A211378: G_n(19), A215409: G_n(3), A222117: G_n(15), A266204: G_n(5), A266205: G_n(6), A271554: G_n(7), A271555: G_n(8), A271556: G_n(9), A266201: G_n(n).
Sequence in context: A014831 A048440 A226202 * A351750 A267031 A289163
KEYWORD
nonn,fini
AUTHOR
Natan Arie Consigli, Apr 11 2016
STATUS
approved

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

License Agreements, Terms of Use, Privacy Policy. .

Last modified March 28 22:04 EDT 2024. Contains 371254 sequences. (Running on oeis4.)