A271554 -id:A271554 - cp's OEIS frontend

A056193 Goodstein sequence starting with 4: to calculate a(n+1), write a(n) in the hereditary representation in base n+2, then bump the base to n+3, then subtract 1.

4, 26, 41, 60, 83, 109, 139, 173, 211, 253, 299, 348, 401, 458, 519, 584, 653, 726, 803, 884, 969, 1058, 1151, 1222, 1295, 1370, 1447, 1526, 1607, 1690, 1775, 1862, 1951, 2042, 2135, 2230, 2327, 2426, 2527, 2630, 2735, 2842, 2951, 3062, 3175, 3290, 3407

Offset: 0

Henry Bottomley, Aug 02 2000

Goodstein's theorem shows that such a sequence converges to zero for any starting value [e.g. if a(0)=1 then a(1)=0; if a(0)=2 then a(3)=0; and if a(0)=3 then a(5)=0]. With a(0)=4 we have a(3*2^(3*2^27 + 27) - 3)=0, which is well beyond the 10^(10^8)-th term.
The second half of such sequences is declining and the previous quarter is stable.
The resulting sequence 0,1,3,5,3*2^402653211 - 3, ... (see Comments in A056041) grows too rapidly to have its own entry.

			a(0) = 4 = 2^2,
a(1) = 3^3 - 1 = 26 = 2*3^2 + 2*3 + 2,
a(2) = 2*4^2 + 2*4 + 2 - 1 = 41 = 2*4^2 + 2*4 + 1,
a(3) = 2*5^2 + 2*5 + 1 - 1 = 60 = 2*5^2 + 2*5,
a(4) = 2*6^2 + 2*6 - 1 = 83 = 2*6^2 + 6 + 5,
a(5) = 2*7^2 + 7 + 5 - 1 = 109 etc.

Reinhard Zumkeller, Table of n, a(n) for n = 0..10000 (final 2 terms from Nicholas Matteo)
R. L. Goodstein, On the Restricted Ordinal Theorem, The Journal of Symbolic Logic, Vol. 9, No. 2 (1944), 33-41.
Eric Weisstein's World of Mathematics, Goodstein Sequence.
Wikipedia, Goodstein's Theorem
Reinhard Zumkeller, Haskell programs for Goodstein sequences

Cf. A056041, A056004, A057650, A059934, A059935, A059936, A271977.

Cf. A215409, A266204, A271554, A222117, A059933, A211378.

Haskell
```
See Zumkeller link
```

lista(nn) = {print1(a = 4, ", "); 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, ", "););} \\ Michel Marcus, Feb 22 2016

Edited by N. J. A. Sloane, Mar 06 2006

Offset changed to 0 by Nicholas Matteo, Sep 04 2019

A215409 The Goodstein sequence G_n(3).

Original entry on oeis.org

3, 3, 3, 2, 1, 0

Offset: 0

Jonathan Sondow, Aug 10 2012

G_0(m) = m. To get the 2nd term, write m in hereditary base 2 notation (see links), change all the 2s to 3s, and then subtract 1 from the result. To get the 3rd term, write the 2nd term in hereditary base 3 notation, change all 3s to 4s, and subtract 1 again. Continue until the result is zero (by Goodstein's Theorem), when the sequence terminates.

Decimal expansion of 33321/100000. - Natan Arie Consigli, Jan 23 2015

			a(0) = 3 = 2^1 + 1;
a(1) = 3^1 + 1 - 1 = 3^1 = 3;
a(2) = 4^1 - 1 = 3;
a(3) = 3 - 1 = 2;
a(4) = 2 - 1 = 1;
a(5) = 1 - 1 = 0.

R. L. Goodstein, On the Restricted Ordinal Theorem, J. Symb. Logic 9, 33-41, 1944.
Eric Weisstein's World of Mathematics, Hereditary Representation
Eric Weisstein's World of Mathematics, Goodstein Sequence
Eric Weisstein's World of Mathematics, Goodstein's Theorem
Wikipedia, Hereditary base-n notation
Wikipedia, Goodstein sequence
Wikipedia, Goodstein's Theorem
Reinhard Zumkeller, Haskell programs for Goodstein sequences

Cf. A056004, A057650, A059934, A059935, A059936, A271977.

Cf. A056041, A056193, A266204, A271554, A222117, A059933, A211378.

Haskell
```
-- See Link
```

PadRight[CoefficientList[Series[3 + 3 x + 3 x^2 + 2 x^3 + x^4, {x, 0, 4}], x], 6] (* Michael De Vlieger, Dec 12 2017 *)

B(n, b)=sum(i=1, #n=digits(n, b), n[i]*(b+1)^if(#nIain Fox, Dec 13 2017

first(n) = my(res = vector(n)); res[1] = res[2] = res[3] = 3; res[4] = 2; res[5] = 1; res; \\ Iain Fox, Dec 12 2017

first(n) = Vec(3 + 3*x + 3*x^2 + 2*x^3 + x^4 + O(x^n)) \\ Iain Fox, Dec 12 2017

a(n) = floor(2 - (4/Pi)*atan(n-3)) \\ Iain Fox, Dec 12 2017

a(0) = a(1) = a(2) = 3; a(3) = 2; a(4) = 1; a(n) = 0, n > 4;
From Iain Fox, Dec 12 2017: (Start)
G.f.: 3 + 3*x + 3*x^2 + 2*x^3 + x^4.
E.g.f.: 3 + 3*x + (3/2)*x^2 + (1/3)*x^3 + (1/24)*x^4.
a(n) = floor(2 - (4/Pi)*arctan(n-3)), n >= 0.
(End)

Corrected by Natan Arie Consigli, Jan 23 2015

A271555 a(n) = G_n(8), where G is the Goodstein function defined in A266201.

Original entry on oeis.org

8, 80, 553, 6310, 93395, 1647195, 33554571, 774841151, 20000000211, 570623341475, 17832200896811, 605750213184854, 22224013651116433, 875787780761719208, 36893488147419103751, 1654480523772673528938, 78692816150593075151501, 3956839311320627178248684

Offset: 0

Natan Arie Consigli, Apr 10 2016

			G_1(8) = B_2(8)-1 = B_2(2^(2+1))-1 = 3^(3+1)-1 = 80;
G_2(8) = B_3(2*3^3+2*3^2+2*3+2)-1 = 2*4^4+2*4^2+2*4+2-1 = 553;
G_3(8) = B_4(2*4^4+2*4^2+2*4+1)-1 = 2*5^5+2*5^2+2*5+1-1 = 6310;
G_4(8) = B_5(2*5^5+2*5^2+2*5)-1 = 2*6^6+2*6^2+2*6-1 = 93395;
G_5(8) = B_6(2*6^6+2*6^2+6+5)-1 = 2*7^7+2*7^2+7+5-1 = 1647195;
G_6(8) = B_7(2*7^7+2*7^2+7+4)-1 = 2*8^8+2*8^2+8+4-1 = 33554571;
G_7(8) = B_8(2*8^8+2*8^2+8+3)-1 = 2*9^9+2*9^2+9+3-1 = 774841151.

Nicholas Matteo, Table of n, a(n) for n = 0..384
R. L. Goodstein, On the Restricted Ordinal Theorem, The Journal of Symbolic Logic 9, no. 2 (1944), 33-41.
Wikipedia, Goodstein sequence

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), A266201: G_n(n).

lista(nn) = {print1(a = 8, ", "); 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, ", "); ); }

a(3) corrected by Nicholas Matteo, Aug 15 2019

A271556 a(n) = G_n(9), where G is the Goodstein function defined in A266201.

Original entry on oeis.org

9, 81, 1023, 9842, 140743, 2471826, 50333399, 1162263921, 30000003325, 855935016215, 26748301350411, 908625319783885, 33336020476682897, 1313681671142588955, 55340232221128667935, 2481720785659010308168, 118039224225889612744771, 5935258966980940767393628

Offset: 0

Natan Arie Consigli, Apr 10 2016

			G_1(9) = B_2(9)-1 = B_2(2^(2+1)+1)-1 = 3^(3+1) + 1-1 = 81;
G_2(9) = B_3(3^(3+1))-1 = 4^(4+1)-1 = 1023;
G_3(9) = B_4(3*4^4 + 3*4^3 + 3*4^2 + 3*4 + 3)-1 = 3*5^5 + 3*5^3 + 3*5^2 + 3*5 + 3-1 = 9842;
G_4(9) = B_5(3*5^5 + 3*5^3 + 3*5^2 + 3*5 + 2)-1 = 3*6^6 + 3*6^3 + 3*6^2 + 3*6 + 2-1 = 140743;
G_5(9) = B_6(3*6^6 + 3*6^3 + 3*6^2 + 3*6 + 1)-1 = 3*7^7 + 3*7^3 + 3*7^2 + 3*7 + 1-1 = 2471826;
G_6(9) = B_7(3*7^7 + 3*7^3 + 3*7^2 + 3*7)-1 = 3*8^8 + 3*8^3 + 3*8^2 + 3*8-1 = 50333399.

Nicholas Matteo, Table of n, a(n) for n = 0..384
R. L. Goodstein, On the Restricted Ordinal Theorem, The Journal of Symbolic Logic 9, no. 2 (1944), 33-41.

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), A266201: G_n(n).

lista(nn) = {print1(a = 9, ", "); 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, ", "); ); }

A271557 a(n) = G_n(10), where G is the Goodstein function defined in A266201.

Original entry on oeis.org

10, 83, 1025, 15625, 279935, 4215754, 84073323, 1937434592, 50000555551, 1426559238830, 44580503598539, 1514375534972427, 55560034130686045, 2189469451908364943, 92233720368553350471, 4136201309431691363859, 196732040376482697880697, 9892098278301567958688175

Offset: 0

Natan Arie Consigli, Apr 11 2016

			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.

Nicholas Matteo, Table of n, a(n) for n = 0..384
R. L. Goodstein, On the Restricted Ordinal Theorem, The Journal of Symbolic Logic 9, no. 2 (1944), 33-41.

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).

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, ", "); ); }

A271558 a(n) = G_n(11), where G is the Goodstein function defined in A266201.

Original entry on oeis.org

11, 84, 1027, 15627, 279937, 5764801, 134217727, 2749609302, 70077777775, 1997331745490, 62412976762503, 2120126221988686, 77784048573561751, 3065257233947460930, 129127208517971179375, 5790681833207409243109, 275424856527080300658781, 13848937589622201728586799

Offset: 0

Natan Arie Consigli, Apr 11 2016

			G_1(11) = B_2(11)-1 = B_2(2^(2+1)+2+1)-1 = 3^(3+1)+3+1-1 = 84;
G_2(11) = B_3(3^(3+1)+3)-1 = 4^(4+1)+4-1 = 1027;
G_3(11) = B_4(4^(4+1)+3)-1 = 5^(5+1)+3-1 = 15627;
G_4(11) = B_5(5^(5+1)+2)-1 = 6^(6+1)+2-1 = 279937;
G_5(11) = B_6(6^(6+1)+1)-1 = 7^(7+1)+1-1 = 5764801;
G_6(11) = B_7(7^(7+1))-1 = 8^(8+1)-1 = 134217727.

Nicholas Matteo, Table of n, a(n) for n = 0..384
R. L. Goodstein, On the Restricted Ordinal Theorem, The Journal of Symbolic Logic 9, no. 2 (1944), 33-41.

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), A271557: G_n(10), A266201: G_n(n).

lista(nn) = {print1(a = 11, ", "); 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, ", "); ); }

a(9)-a(13) corrected by Nicholas Matteo, Aug 15 2019

a(14) onwards from Nicholas Matteo, Aug 28 2019

A271559 a(n) = G_n(12), where G is the Goodstein function defined in A266201.

Original entry on oeis.org

12, 107, 1065, 15685, 280019, 5764910, 134217867, 3486784574, 100000000211, 3138428376974, 106993205379371, 3937376385699637, 155568095557812625, 6568408355712891083, 295147905179352826375, 14063084452067724991593, 708235345355337676358285, 37589973457545958193356327

Offset: 0

Natan Arie Consigli, Apr 11 2016

Goodstein's theorem shows that such sequence converges to zero for any starting value.

			G_1(12) = B_2(12)-1 = B_2(2^(2+1)+2^2)-1 = 3^(3+1)+3^3-1 = 107;
G_2(12) = B_3(3^(3+1)+2*3^2+2*3+2)-1 = 4^(4+1)+2*4^2+2*4+2-1 = 1065;
G_3(12) = B_4(4^(4+1)+2*4^2+2*4+1)-1 = 5^(5+1)+2*5^2+2*5+1-1 = 15685;
G_4(12) = B_5(5^(5+1)+2*5^2+2*5)-1 = 6^(6+1)+2*6^2+2*6-1 = 280019;
G_5(12) = B_6(6^(6+1)+2*6^2+6+5)-1 = 7^(7+1)+2*7^2+7+5-1 = 5764910;
G_6(12) = B_7(7^(7+1)+2*7^2+7+4)-1 = 8^(8+1)+2*8^2+8+4-1 = 134217867;
G_7(12) = B_8(8^(8+1)+2*8^2+8+3)-1 = 9^(9+1)+2*9^2+9+3-1 = 3486784574.

Nicholas Matteo, Table of n, a(n) for n = 0..383
R. L. Goodstein, On the Restricted Ordinal Theorem, The Journal of Symbolic Logic 9, no. 2 (1944), 33-41.

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), A271557: G_n(10), A271558: G_n(11), A266201: G_n(n).

lista(nn) = {print1(a = 12, ", "); 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, ", "); ); }

A271560 a(n) = G_n(13), where G is the Goodstein function defined in A266201.

Original entry on oeis.org

13, 108, 1279, 16092, 280711, 5765998, 134219479, 3486786855, 100000003325, 3138428381103, 106993205384715, 3937376385706415, 155568095557821073, 6568408355712901455, 295147905179352838943, 14063084452067725006646, 708235345355337676376131, 37589973457545958193377292

Offset: 0

Natan Arie Consigli, Apr 11 2016

			G_1(13) = B_2(13)-1 = B_2(2^(2+1)+2^2+1)-1 = 3^(3+1)+3^3+1-1 = 108;
G_2(13) = B_3(3^(3+1)+3^3)-1 = 4^(4+1)+4^4-1 = 1279;
G_3(13) = B_4(4^(4+1)+3*4^3+3*4^2+3*4+3)-1 = 5^(5+1)+3*5^3+3*5^2+3*5+3-1 = 16092;
G_4(13) = B_5(5^(5+1)+3*5^3+3*5^2+3*5+2)-1 = 6^(6+1)+3*6^3+3*6^2+3*6+2-1 = 280711;
G_5(13) = B_6(6^(6+1)+3*6^3+3*6^2+3*6+1)-1 = 7^(7+1)+3*7^3+3*7^2+3*7+1-1 = 5765998;
G_6(13) = B_7(7^(7+1)+3*7^3+3*7^2+3*7)-1 = 8^(8+1)+3*8^3+3*8^2+3*8-1 = 134219479;
G_7(13) = B_8(8^(8+1)+3*8^3+3*8^2+2*8+7)-1 = 9^(9+1)+3*9^3+3*9^2+2*9+7-1 = 3486786855.

Nicholas Matteo, Table of n, a(n) for n = 0..383

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), A271557: G_n(10), A271558: G_n(11), A271559: G_n(12), A266201: G_n(n).

lista(nn) = {my(a=13); print1(a, ", "); for (n=2, nn, my(pd = Pol(digits(a, n)), q = sum(k=0, poldegree(pd), my(c=polcoeff(pd, k)); if (c, c*x^subst(Pol(digits(k, n)), x, n+1), 0))); a = subst(q, x, n+1) - 1; print1(a, ", "); ); }

A271561 a(n) = G_n(14), where G is the Goodstein function defined in A266201.

Original entry on oeis.org

14, 110, 1281, 18750, 326591, 5862840, 134404971, 3487116548, 100000555551, 3138429262496, 106993206736331, 3937376387710451, 155568095560708189, 6568408355716958693, 295147905179358418247, 14063084452067732533983, 708235345355337686361209, 37589973457545958206423881

Offset: 0

Natan Arie Consigli, Apr 13 2016

			G_1(14) = B_2(14)-1 = B_2(2^(2+1)+2^2+2)-1 = 3^(3+1)+3^3+3-1 = 110;
G_2(14) = B_3(3^(3+1)+3^3+2)-1 = 4^(4+1)+4^4+2-1 = 1281;
G_3(14) = B_4(4^(4+1)+4^4+1)-1 = 5^(5+1)+5^5+1-1 = 18750;
G_4(14) = B_5(5^(5+1)+5^5)-1 = 6^(6+1)+6^6-1 = 326591.

Nicholas Matteo, Table of n, a(n) for n = 0..383

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), A271557: G_n(10), A271558: G_n(11), A271559: G_n(12), A271560: G_n(13), A266201: G_n(n).

lista(nn) = {print1(a = 14, ", "); 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, ", "); ); }

A271988 g_n(7) where g is the weak Goodstein function defined in A266202.

Original entry on oeis.org

7, 12, 19, 27, 37, 49, 63, 69, 75, 81, 87, 93, 99, 105, 111, 116, 121, 126, 131, 136, 141, 146, 151, 156, 161, 166, 171, 176, 181, 186, 191, 195, 199, 203, 207, 211, 215, 219, 223, 227, 231, 235, 239, 243, 247, 251, 255, 259, 263, 267, 271, 275, 279, 283, 287, 291, 295, 299, 303, 307, 311, 315, 319, 322, 325

Offset: 0

Natan Arie Consigli, May 21 2016

For more info see A266201-A266202.

			g_1(7)= b_2(7)-1 = b_2(2^2+2+1)-1 = 3^2+3+1-1 = 12;
g_2(7) = b_3(3^2+3)-1 = 4^2+4-1 = 19;
g_3(7) = b_4(4^2+3)-1 = 5^2+3-1 = 27;
g_4(7) = b_5(5^2+2)-1 = 6^2+2-1 = 37;
g_5(7) = b_6(6^2+1)-1 = 7^2+1-1 = 49;
g_6(7) = b_7(7^2)-1 = 8^2-1 = 63;
g_7(7) = b_8(7*8+7)-1 = 7*9+7-1 = 69;
...
g_2045(7) = 0.

Cf. A271554: G_n(7).

Weak Goodstein sequences: A137411: g_n(11); A265034: g_n(266); A267647: g_n(4); A267648: g_n(5); A271987: g_n(6); A266202: g_n(n); A266203: a(n)=k such that g_k(n)=0;

g[k_, n_] := If[k == 0, n, Total@ Flatten@ MapIndexed[#1 (k + 2)^(#2 - 1) &, Reverse@ IntegerDigits[#, k + 1]] &@ g[k - 1, n] - 1]; Table[g[n, 7], {n, 0, 64}]

cp's OEIS Frontend

A056193 Goodstein sequence starting with 4: to calculate a(n+1), write a(n) in the hereditary representation in base n+2, then bump the base to n+3, then subtract 1.

Views

Author

Keywords

Comments

Examples

Links

Crossrefs

Programs

Haskell

PARI

Extensions

A215409 The Goodstein sequence G_n(3).

Views

Author

Keywords

Comments

Examples

Links

Crossrefs

Programs

Haskell

Mathematica

PARI

PARI

PARI

PARI

Formula

Extensions

A271555 a(n) = G_n(8), where G is the Goodstein function defined in A266201.

Views

Author

Keywords

Examples

Links

Crossrefs

Programs

PARI

Extensions

A271556 a(n) = G_n(9), where G is the Goodstein function defined in A266201.

Views

Author

Keywords

Examples

Links

Crossrefs

Programs

PARI

A271557 a(n) = G_n(10), where G is the Goodstein function defined in A266201.

Views

Author

Keywords

Examples

Links

Crossrefs

Programs

PARI

A271558 a(n) = G_n(11), where G is the Goodstein function defined in A266201.

Views

Author

Keywords

Examples

Links

Crossrefs

Programs

PARI

Extensions

A271559 a(n) = G_n(12), where G is the Goodstein function defined in A266201.

Views

Author

Keywords

Comments

Examples

Links

Crossrefs

Programs

PARI

A271560 a(n) = G_n(13), where G is the Goodstein function defined in A266201.

Views