A132038 -id:A132038 - cp's OEIS frontend

A028672 Pseudo Galois numbers for d=10.

1, 90, 891000, 890109000000, 89001998910000000000, 890011088900109000000000000000, 890010198889020099891000000000000000000000, 89001010988800021098899001090000000000000000000000000000, 890010100987899112108987901010099891000000000000000000000000000000000000

Offset: 0

Olivier Gérard

nonn

Vincenzo Librandi, Table of n, a(n) for n = 0..31

Cf. A028668, A028670, A028671, A028674, A028676, A028677, A028678, A028680, A028682, A028683, A028684, A028686.

Cf. A132038.

FoldList[ #1*10^#2 (10^#2-1)&, 1, Range[ 20 ] ]
a[n_] := 10^n * Product[10^n - 10^k, {k, 0, n-1}]; Array[a, 9, 0] (* Amiram Eldar, Jul 13 2025 *)

a(n) = 10^n * prod(k = 0, n-1, 10^n - 10^k); \\ Amiram Eldar, Jul 13 2025

a(n) = 10^n * Product_{k=0..n-1} (10^n - 10^k).

a(n) ~ c * 10^(n^2+n), where c = A132038. - Amiram Eldar, Jul 13 2025

A132035 Decimal expansion of Product_{k>0} (1-1/7^k).

Original entry on oeis.org

8, 3, 6, 7, 9, 5, 4, 0, 7, 0, 8, 9, 0, 3, 7, 8, 7, 1, 0, 2, 6, 7, 2, 9, 7, 9, 8, 1, 4, 6, 1, 3, 6, 2, 4, 1, 3, 5, 2, 4, 3, 6, 4, 3, 5, 8, 7, 6, 7, 1, 6, 5, 1, 9, 9, 6, 4, 1, 1, 5, 1, 0, 1, 7, 7, 0, 0, 9, 1, 6, 0, 1, 2, 6, 5, 4, 2, 7, 6, 0, 5, 8, 7, 8, 7, 5, 5, 5, 4, 2, 8, 4, 9, 0, 5, 1, 2, 0, 2, 1, 7, 5, 3

Offset: 0

Hieronymus Fischer, Aug 14 2007

			0.8367954070890378710...

Richard J. McIntosh, Some Asymptotic Formulae for q-Hypergeometric Series, Journal of the London Mathematical Society, Vol. 51, No. 1 (1995), pp. 120-136; alternative link.

Cf. A027875, A048651, A100220, A132023, A132026, A132038, A098844, A067080, A000203.

digits = 103; NProduct[1-1/7^k, {k, 1, Infinity}, NProductFactors -> 200, WorkingPrecision -> digits+3] // N[#, digits+3]& // RealDigits[#, 10, digits]& // First (* Jean-François Alcover, Feb 18 2014 *)
RealDigits[QPochhammer[1/7], 10, 100][[1]] (* Amiram Eldar, May 09 2023 *)

prodinf(k=1, 1 - 1/(7^k)) \\ Amiram Eldar, May 09 2023

Equals exp(-Sum_{n>0} sigma_1(n)/(n*7^n)) = exp(-Sum_{n>0} A000203(n)/(n*7^n)).
From Amiram Eldar, May 09 2023: (Start)
Equals sqrt(2*Pi/log(7)) * exp(log(7)/24 - Pi^2/(6*log(7))) * Product_{k>=1} (1 - exp(-4*k*Pi^2/log(7))) (McIntosh, 1995).
Equals Sum_{n>=0} (-1)^n/A027875(n). (End)

A259147 Decimal expansion of phi(exp(-Pi/2)), where phi(q) = Product_{n>=1} (1-q^n) is the Euler modular function.

Original entry on oeis.org

7, 4, 9, 3, 1, 1, 4, 7, 7, 8, 0, 0, 0, 0, 2, 7, 8, 7, 4, 2, 9, 6, 2, 5, 6, 5, 8, 7, 8, 3, 3, 8, 0, 3, 1, 1, 9, 0, 4, 0, 9, 2, 5, 2, 7, 9, 0, 1, 1, 7, 3, 9, 2, 8, 3, 1, 2, 0, 6, 7, 3, 1, 0, 1, 3, 1, 3, 5, 8, 8, 5, 3, 7, 5, 5, 1, 7, 4, 7, 2, 5, 8, 6, 1, 3, 4, 7, 5, 6, 3, 5, 7, 6, 5, 5, 8, 5, 8, 4, 0, 4, 6, 3, 7, 9

Offset: 0

Jean-François Alcover, Jun 19 2015

			0.74931147780000278742962565878338031190409252790117392831206731...

Istvan Mezo, Several special values of Jacobi theta functions, arXiv:1106.2703 [math.CA], 2011-2013.
Eric Weisstein's MathWorld, Infinite Product
Eric Weisstein's MathWorld, Jacobi Theta Functions
Eric Weisstein's MathWorld, q-Pochhammer Symbol
Wikipedia, Euler function

Cf. A048651 phi(1/2), A100220 phi(1/3), A100221 phi(1/4), A100222 phi(1/5), A132034 phi(1/6), A132035 phi(1/7), A132036 phi(1/8), A132037 phi(1/9), A132038 phi(1/10), A368211 phi(exp(-Pi/16)), A292862 phi(exp(-Pi/8)), A292863 phi(exp(-Pi/4)), A259148 phi(exp(-Pi)), A259149 phi(exp(-2*Pi)), A292888 phi(exp(-3*Pi)), A259150 phi(exp(-4*Pi)), A292905 phi(exp(-5*Pi)), A363018 phi(exp(-6*Pi)), A259151 phi(exp(-8*Pi)), A363019 phi(exp(-10*Pi)), A363020 phi(exp(-12*Pi)), A292864 phi(exp(-16*Pi)), A363021 phi(exp(-20*Pi)).

Cf. A292819, A292823, A292827.

phi[q_] := QPochhammer[q, q]; RealDigits[phi[Exp[-Pi/2]], 10, 105] // First

phi(q) = QPochhammer(q,q) = (q;q)_infinity.
phi(q) also equals theta'(1, 0, sqrt(q))^(1/3)/(2^(1/3)*q^(1/24)), where theta' is the derivative of the elliptic theta function theta(a,u,q) w.r.t. u.
phi(exp(-Pi/2)) = ((sqrt(2) - 1)^(1/3)*(4 + 3*sqrt(2))^(1/24) * exp(Pi/48) * Gamma(1/4))/(2^(5/6)*Pi^(3/4)).
phi(exp(-Pi/2)) = (sqrt(2)-1)^(1/4) * exp(Pi/48) * Gamma(1/4)/(2^(13/16)*Pi^(3/4)). - Vaclav Kotesovec, Jul 03 2017

A015009 q-factorial numbers for q=10.

Original entry on oeis.org

1, 1, 11, 1221, 1356531, 15072415941, 1674711207620451, 1860790044610366931061, 20675444733360738721748118771, 2297271634742810443154153338805764581, 2552524038347870310755413660544832496799359491, 28361378203581611893021499527080870668821235178133404501

Offset: 0

Olivier Gérard

Vincenzo Librandi, Table of n, a(n) for n = 0..40
Index entries for sequences related to factorial numbers.

Cf. A015001, A015002, A015004, A015005, A015006, A015007, A015008, A015011.
Column q=10 of A069777.
Cf. A002275, A132038.

[n le 1 select 1 else (10^n-1)*Self(n-1)/9: n in [1..15]]; // Vincenzo Librandi, Oct 26 2012

RecurrenceTable[{a[1]==1, a[n]==((10^n-1) * a[n-1])/9}, a, {n, 15}] (* Vincenzo Librandi, Oct 26 2012 *)
Table[QFactorial[n, 10], {n, 15}] (* Bruno Berselli, Aug 14 2013 *)

a(n) = Product_{k=1..n} (q^k - 1)/(q - 1) with q=10.
a(0) = 1, a(n) = (10^n - 1)*a(n-1)/9. - Vincenzo Librandi, Oct 26 2012
From Amiram Eldar, Jul 05 2025: (Start)
a(n) = Product_{k=1..n} A002275(k).
a(n) ~ c * 10^(n*(n+1)/2)/9^n, where c = A132038. (End)

a(0)=1 prepended by Alois P. Heinz, Sep 08 2021

A132265 Decimal expansion of Product_{k>=0} (1 - 1/(2*11^k)).

Original entry on oeis.org

4, 7, 5, 1, 0, 4, 1, 2, 7, 5, 0, 7, 6, 0, 3, 1, 0, 5, 3, 9, 7, 5, 6, 4, 4, 4, 7, 2, 9, 4, 6, 9, 7, 6, 9, 4, 3, 3, 6, 9, 7, 1, 9, 2, 1, 1, 7, 0, 8, 5, 1, 1, 6, 3, 8, 0, 0, 7, 7, 3, 6, 6, 5, 4, 1, 3, 0, 4, 7, 5, 4, 4, 5, 7, 2, 4, 8, 7, 7, 3, 7, 2, 3, 0, 8, 4, 3, 7, 6, 9, 3, 7, 4, 4, 1, 6, 8, 2, 4, 9, 8, 2, 2, 7, 3

Offset: 0

Hieronymus Fischer, Aug 20 2007

			0.47510412750760310539756444...

G. C. Greubel, Table of n, a(n) for n = 0..1500
Eric Weisstein's World of Mathematics, q-Pochhammer Symbol

Cf. A000217, A132019-A132026, A132034-A132038, A132263, A132266-A132268, A132323-A132326.

digits = 105; NProduct[1-1/(2*11^k), {k, 0, Infinity}, NProductFactors -> 100, WorkingPrecision -> digits+10] // N[#, digits+10]& // RealDigits[#, 10, digits]& // First (* Jean-François Alcover, Feb 18 2014 *)
N[QPochhammer[1/2,1/11]] (* G. C. Greubel, Nov 30 2015 *)

prodinf(x=0, 1 - 1/(2*11^x)) \\ Altug Alkan, Dec 01 2015

lim inf Product_{k=0..floor(log_11(n))} floor(n/11^k)*11^k/n for n-->oo.
lim inf A132263(n)*11^((1+floor(log_11(n)))*floor(log_11(n))/2)/n^(1+floor(log_11(n))) for n-->oo.
lim inf A132263(n)*11^A000217(floor(log_11(n)))/n^(1+floor(log_11(n))) for n-->oo.
(1/2)*exp(-Sum_{n>0} 11^(-n)*Sum_{k|n} 1/(k*2^k)).
lim inf A132263(n)/A132263(n+1) = 0.47510412750760310539756444... for n-->oo.
Equals (1/2; 1/11){infinity}, where (a;q){infinity} is the q-Pochhammer symbol. - G. C. Greubel, Nov 30 2015

A132268 Decimal expansion of Product_{k>0} (1-1/12^k).

Original entry on oeis.org

9, 0, 9, 7, 2, 6, 2, 6, 8, 9, 0, 5, 9, 9, 4, 8, 8, 8, 6, 3, 6, 3, 6, 2, 0, 4, 6, 9, 7, 7, 0, 8, 0, 2, 4, 9, 1, 2, 0, 7, 9, 1, 6, 9, 1, 9, 4, 1, 0, 1, 4, 2, 7, 4, 3, 2, 6, 1, 5, 4, 4, 4, 1, 2, 8, 6, 9, 0, 2, 4, 5, 7, 6, 6, 1, 9, 5, 4, 1, 6, 2, 0, 2, 6, 0, 0, 0, 5, 5, 3, 8, 8, 8, 8, 1, 0, 8, 5, 1, 4, 8, 3, 9, 7, 1, 9

Offset: 0

Hieronymus Fischer, Aug 20 2007

			0.9097262689059948886363620469770...

G. C. Greubel, Table of n, a(n) for n = 0..1200
Richard J. McIntosh, Some Asymptotic Formulae for q-Hypergeometric Series, Journal of the London Mathematical Society, Vol. 51, No. 1 (1995), pp. 120-136; alternative link.

Cf. A027880, A048651, A100220, A132019-A132026, A132034-A132038, A132265-A132267, A132323-A132326, A000203.

digits = 106; NProduct[1-1/12^k, {k, 1, Infinity}, NProductFactors -> 100, WorkingPrecision -> digits+3] // N[#, digits+3]& // RealDigits[#, 10, digits]& // First (* Jean-François Alcover, Feb 18 2014 *)
N[QPochhammer[1/12,1/12]] (* G. C. Greubel, Dec 05 2015 *)

prodinf(k=1, (1-1/12^k)) \\ Michel Marcus, Dec 05 2015

Equals exp(-Sum_{n>0} sigma_1(n)/(n*12^n)) = exp(-Sum_{n>0} A000203(n)/(n*12^n)).
Equals (1/12; 1/12){infinity}, where (a;q){infinity} is the q-Pochhammer symbol. - G. C. Greubel, Dec 05 2015
From Amiram Eldar, May 09 2023: (Start)
Equals sqrt(2*Pi/log(12)) * exp(log(12)/24 - Pi^2/(6*log(12))) * Product_{k>=1} (1 - exp(-4*k*Pi^2/log(12))) (McIntosh, 1995).
Equals Sum_{n>=0} (-1)^n/A027880(n). (End)

A132326 Decimal expansion of Product_{k>=1} (1+1/10^k).

Original entry on oeis.org

1, 1, 1, 2, 2, 3, 4, 5, 6, 9, 1, 3, 7, 0, 5, 0, 6, 3, 2, 1, 2, 6, 0, 7, 8, 0, 6, 7, 0, 9, 4, 4, 0, 5, 8, 0, 3, 7, 4, 7, 5, 0, 7, 4, 6, 7, 5, 7, 7, 5, 9, 2, 8, 3, 5, 7, 8, 7, 9, 5, 8, 2, 3, 7, 0, 3, 3, 2, 5, 3, 4, 6, 9, 4, 8, 8, 1, 4, 1, 1, 0, 4, 3, 7, 6, 4, 7, 2, 2, 2, 2, 6, 4, 2, 1, 3, 5, 2, 3, 5, 5, 6, 4, 7, 4

Offset: 1

Hieronymus Fischer, Aug 20 2007

Half the constant A132325.

			1.1122345691370506321260780670944...

G. C. Greubel, Table of n, a(n) for n = 1..1200
Richard J. McIntosh, Some Asymptotic Formulae for q-Hypergeometric Series, Journal of the London Mathematical Society, Vol. 51, No. 1 (1995), pp. 120-136; alternative link.

Cf. A000593, A067080, A079555, A132019-A132026, A132034-A132038, A132265-A132268, A132271, A132272, A132325.

digits = 105; NProduct[1+1/3^k, {k, 0, Infinity}, NProductFactors -> 100, WorkingPrecision -> digits+3] // N[#, digits+3]& // RealDigits[#, 10, digits]& // First (* Jean-François Alcover, Feb 18 2014 *)
N[QPochhammer[-1/10,1/10]] (* G. C. Greubel, Dec 01 2015 *)

prodinf(k=1, 1+1/10^k) \\ Amiram Eldar, May 20 2023

Equals (1/2)*lim sup_{n->oo} Product_{0<=k<=floor(log_10(n))} (1+1/floor(n/10^k)).
Equals (1/2)*lim sup_{n->oo} A132271(n)/n^((1+log_10(n))/2).
Equals (1/2)*lim sup_{n->oo} A132272(n)/n^((log_10(n)-1)/2).
Equals exp(Sum_{n>0} 10^(-n)*Sum_{k|n} -(-1)^k/k) = exp(Sum_{n>0} A000593(n)/(n*10^n)).
Equals (1/2)*lim sup_{n->oo} A132271(n+1)/A132271(n).
Equals (-1/10; 1/10){infinity}, where (a;q){infinity} is the q-Pochhammer symbol. - G. C. Greubel, Dec 01 2015
Equals (sqrt(2)/2) * exp(log(10)/24 + Pi^2/(12*log(10))) * Product_{k>=1} (1 - exp(-2*(2*k-1)*Pi^2/log(10))) (McIntosh, 1995). - Amiram Eldar, May 20 2023

A132267 Decimal expansion of Product_{k>0} (1-1/11^k).

Original entry on oeis.org

9, 0, 0, 8, 3, 2, 7, 0, 6, 8, 0, 9, 7, 1, 5, 2, 7, 9, 9, 4, 9, 8, 6, 2, 6, 9, 4, 7, 6, 0, 6, 4, 7, 7, 4, 4, 7, 6, 2, 4, 9, 1, 1, 9, 2, 2, 1, 6, 6, 3, 9, 5, 2, 4, 0, 2, 1, 4, 6, 1, 7, 2, 4, 8, 8, 0, 6, 5, 7, 0, 8, 7, 0, 6, 7, 0, 9, 7, 5, 8, 5, 6, 7, 0, 0, 1, 6, 3, 9, 2, 9, 9, 1, 9, 9, 2, 8, 3, 5, 6, 4, 6, 5, 2, 0

Offset: 0

Hieronymus Fischer, Aug 20 2007

			0.900832706809715279949862694760...

G. C. Greubel, Table of n, a(n) for n = 0..2000
Richard J. McIntosh, Some Asymptotic Formulae for q-Hypergeometric Series, Journal of the London Mathematical Society, Vol. 51, No. 1 (1995), pp. 120-136; alternative link.

Cf. A000203, A027879, A048651, A100220, A132019-A132026, A132034-A132038, A132265-A132268, A132323, A132324, A132325, A132326.

digits = 105; NProduct[1-1/11^k, {k, 1, Infinity}, NProductFactors -> 100, WorkingPrecision -> digits+3] // N[#, digits+3]& // RealDigits[#, 10, digits]& // First (* Jean-François Alcover, Feb 18 2014 *)
N[QPochhammer[1/11, 1/11], 200] (* G. C. Greubel, Dec 20 2015 *)

prodinf(x=1, 1-1/11^x) \\ Altug Alkan, Dec 20 2015

Equals exp(-Sum_{n>0} sigma_1(n)/(n*11^n)) = exp(-Sum_{n>0} A000203(n)/(n*11^n)).
Equals (1/11; 1/11){infinity}, where (a;q){infinity} is the q-Pochhammer symbol. - G. C. Greubel, Dec 20 2015
From Amiram Eldar, May 09 2023: (Start)
Equals sqrt(2*Pi/log(11)) * exp(log(11)/24 - Pi^2/(6*log(11))) * Product_{k>=1} (1 - exp(-4*k*Pi^2/log(11))) (McIntosh, 1995).
Equals Sum_{n>=0} (-1)^n/A027879(n). (End)

A132271 Product{k>=0, 1+floor(n/10^k)}.

Original entry on oeis.org

1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 22, 24, 26, 28, 30, 32, 34, 36, 38, 40, 63, 66, 69, 72, 75, 78, 81, 84, 87, 90, 124, 128, 132, 136, 140, 144, 148, 152, 156, 160, 205, 210, 215, 220, 225, 230, 235, 240, 245, 250, 306, 312, 318, 324, 330, 336, 342, 348, 354, 360, 427

Offset: 0

Hieronymus Fischer, Aug 20 2007

nonn

If n is written in base-10 as n=d(m)d(m-1)d(m-2)...d(2)d(1)d(0) (where d(k) is the digit at position k) then a(n) is also the product (1+d(m)d(m-1)d(m-2)...d(2)d(1)d(0))*(1+d(m)d(m-1)d(m-2)...d(2)d(1))*(1+d(m)d(m-1)d(m-2)...d(2))*...*(1+d(m)d(m-1)d(m-2))*(1+d(m)d(m-1))*(1+d(m)).

			a(12)=(1+floor(12/10^0))*(1+floor(12/10^1))=13*2=26; a(21)=63 since 21=21(base-10) and so
a(21)=(1+21)*(1+2)(base-10)=22*3=66.

Cf. A132038, A132325, A132269(p=2), A132327(p=3), A132272.

For the product of terms floor(n/p^k) see A098844, A067080, A132027-A132033, A132263, A132264.

f[n_] := Block[{k = 0, p = 1}, While[a = Floor[n/10^k]; a > 0, p *= 1 + a; k++]; p]; Array[f, 61, 0] (* Robert G. Wilson v, May 10 2011 *)
Table[Product[1+Floor[n/10^k],{k,0,n}],{n,0,60}] (* Harvey P. Dale, May 14 2019 *)

The following formulas are given for a general parameter p considering the product of terms 1+floor(n/p^k) for 0<=k<=floor(log_p(n)), where p=10 for this sequence.
Recurrence: a(n)=(1+n)*a(floor(n/p)); a(pn)=(1+pn)*a(n); a(n*p^m)=product{1<=k<=m, 1+n*p^k}*a(n).
a(k*p^m-j)=(k*p^m-j+1)*k^m*p^(m(m-1)/2), for 0=1, a(p^m)=p^(m(m+1)/2)*product{0<=k<=m, 1+1/p^k}, m>=1.
a(n)=A132272(p*n)=(1+n)*A132272(n).
Asymptotic behavior: a(n)=O(n^((1+log_p(n))/2)); this follows from the inequalities below.
a(n)<=A067080(n)*product{0<=k<=floor(log_p(n)), 1+1/p^k}.
a(n)>=A067080(n)/product{1<=k<=floor(log_p(n)), 1-1/p^k}.
a(n)A000217(log_p(n)), where c=product{k>=0, 1+1/p^k}=2.2244691382741012... (for p=10 see constant A132325).
a(n)>n^((1+log_p(n))/2)=p^A000217(log_p(n)).
lim sup a(n)/A067080(n)=2*product{k>0, 1+1/p^k}=2.2244691382741012..., for n-->oo (for p=10 see constant A132325).
lim inf a(n)/A067080(n)=1/product{k>0, 1-1/p^k}=1/0.8900100999989990000001000..., for n-->oo (for p=10 see constant A132038).
lim inf a(n)/n^((1+log_p(n))/2)=1, for n-->oo.
lim sup a(n)/n^((1+log_p(n))/2)=2*product{k>0, 1+1/p^k}=2.2244691382741012..., for n-->oo (for p=10 see constant A132325).
lim inf a(n+1)/a(n)=2*product{k>0, 1+1/p^k}=2.2244691382741012... for n-->oo (for p=10 see constant A132325).

A132324 Decimal expansion of Product_{k>=1} (1+1/3^k).

Original entry on oeis.org

1, 5, 6, 4, 9, 3, 4, 0, 1, 8, 5, 6, 7, 0, 1, 1, 5, 3, 7, 9, 3, 8, 8, 4, 9, 1, 0, 6, 7, 2, 8, 8, 3, 5, 4, 1, 6, 5, 6, 9, 4, 2, 5, 9, 1, 9, 8, 9, 5, 0, 3, 5, 0, 0, 9, 4, 9, 6, 7, 2, 1, 0, 2, 9, 9, 2, 3, 0, 2, 1, 1, 0, 7, 2, 5, 8, 0, 9, 6, 7, 6, 6, 9, 3, 9, 0, 3, 6, 6, 0, 3, 6, 7, 7, 2, 9, 6, 3, 8, 8, 1, 5, 2, 6, 0

Offset: 1

Hieronymus Fischer, Aug 20 2007

Half the constant A132323.

			1.56493401856701153793884910...

G. C. Greubel, Table of n, a(n) for n = 1..1200
Richard J. McIntosh, Some Asymptotic Formulae for q-Hypergeometric Series, Journal of the London Mathematical Society, Vol. 51, No. 1 (1995), pp. 120-136; alternative link.

Cf. A027871, A079555, A100220, A132019-A132026, A132034-A132038, A132265-A132268, A132323-A132326, A132327, A132328, A000593.

digits = 105; NProduct[1+1/3^k, {k, 1, Infinity}, NProductFactors -> 100, WorkingPrecision -> digits+5] // N[#, digits+5]& // RealDigits[#, 10, digits]& // First (* Jean-François Alcover, Feb 18 2014 *)
N[QPochhammer[-1/3,1/3]] (* G. C. Greubel, Dec 01 2015 *)

(1/2)*lim sup Product{k=0..floor(log_3(n))} (1+1/floor(n/3^k)) for n-->oo.
(1/2)*lim sup A132327(n)/A132027(n) for n-->oo.
(1/2)*lim sup A132327(n)/n^((1+log_3(n))/2) for n-->oo.
(1/2)*lim sup A132328(n)/n^((log_3(n)-1)/2) for n-->oo.
exp(Sum_{n>0} 3^(-n)*Sum_{k|n} -(-1)^k/k) = exp(Sum_{n>0} A000593(n)/(n*3^n)).
(1/2)*lim sup A132327(n+1)/A132327(n) = 1.56493401856701153793884910... for n-->oo.
Equals (-1/3; 1/3){infinity}, where (a;q){infinity} is the q-Pochhammer symbol. - G. C. Greubel, Dec 01 2015
From Amiram Eldar, Feb 19 2022: (Start)
Equals (sqrt(2)/2) * exp(log(3)/24 + Pi^2/(12*log(3))) * Product_{k>=1} (1 - exp(-2*(2*k-1)*Pi^2/log(3))) (McIntosh, 1995).
Equals Sum_{n>=0} 1/A027871(n). (End)

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A028672 Pseudo Galois numbers for d=10.

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A132035 Decimal expansion of Product_{k>0} (1-1/7^k).

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A259147 Decimal expansion of phi(exp(-Pi/2)), where phi(q) = Product_{n>=1} (1-q^n) is the Euler modular function.

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A015009 q-factorial numbers for q=10.

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A132265 Decimal expansion of Product_{k>=0} (1 - 1/(2*11^k)).

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A132268 Decimal expansion of Product_{k>0} (1-1/12^k).

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A132326 Decimal expansion of Product_{k>=1} (1+1/10^k).

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A132267 Decimal expansion of Product_{k>0} (1-1/11^k).

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