Tim Honeywill has authored 3 sequences.
A098438
Numbers k such that (30^k - 1)/29 is prime.
Original entry on oeis.org
2, 5, 11, 163, 569, 1789, 8447, 72871, 78857, 82883
Offset: 1
Searching in the OEIS for 'repunit' gives many similar sequences.
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for i in [1..500] do if i mod 50 eq 0 then print "counter equals", counter; end if; if IsPrime(i) then n := 0; for j in [0..i-1] do n +:= 30^j; end for; if IsPrime(n) then print n; print i; end if; end if; end for;
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Do[If[PrimeQ[(30^n - 1)/29], Print[n]], {n, 1, 10000}] (* Ryan Propper, Jun 25 2005 *)
Select[Prime[Range[100]],PrimeQ[(30^#-1)/29]&] (* Alexander Adamchuk, Feb 11 2007 *)
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is(n)=n=(30^n-1)/29;denominator(n)==1&&ispseudoprime(n) \\ Charles R Greathouse IV, Jul 01 2013
a(5)-a(7), corresponding to probable primes, from
Ryan Propper, Jun 25 2005
Edited by
N. J. A. Sloane Jan 25 2008 at the suggestion of Herman Jamke (hermanjamke(AT)fastmail.fm)
A080254
For n>3, a(n) is the number of elements in the Coxeter complex of type D_n (although the sequence starts at n=0. See comments below for precise explanation).
Original entry on oeis.org
1, 1, 9, 75, 865, 12483, 216113, 4364979, 100757313, 2616517443, 75496735057, 2396212835283, 82968104980961, 3112139513814243, 125716310807844081, 5441108944839913587, 251195548533025953409, 12321551453507301079683
Offset: 0
- Kenneth S. Brown, Buildings, Springer-Verlag, 1988
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CoefficientList[Series[(2*x-E^x)/(E^(2*x)-2), {x, 0, 20}], x]* Range[0, 20]! (* Vaclav Kotesovec, Oct 08 2013 *)
More terms from Antonio G. Astudillo (afg_astudillo(AT)hotmail.com), Feb 14 2003
A080253
a(n) is the number of elements in the Coxeter complex of type B_n (or C_n).
Original entry on oeis.org
1, 3, 17, 147, 1697, 24483, 423857, 8560947, 197613377, 5131725123, 148070287697, 4699645934547, 162723741209057, 6103779096411363, 246564971326084337, 10671541841672056947, 492664975795819140737, 24166020791610523843203
Offset: 0
a(2)=17 as follows. Let (W,S) be a Coxeter system of type B_2. By definition the elements of the associated complex are right cosets of "special parabolic subgroups". These are simply the subgroups generated by subsets of S. In our case they have orders 1,2,2,8 and hence have 8,4,4,1 cosets respectively, giving a total of 17.
- Kenneth S. Brown, Buildings, Springer-Verlag, 1989.
- Vincenzo Librandi, Table of n, a(n) for n = 0..200
- Paul Barry, General Eulerian Polynomials as Moments Using Exponential Riordan Arrays, Journal of Integer Sequences, 16 (2013), #13.9.6.
- Peter C. Fishburn, Signed Orders, Choice Probabilities and Linear Polytopes, Journal of Mathematical Psychology, Volume 45, Issue 1, (2001), pp. 53-80.
- Joël Gay and Vincent Pilaud, The weak order on Weyl posets, arXiv:1804.06572 [math.CO], 2018.
- Eric Weisstein's MathWorld, Polylogarithm.
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A080253 := proc(n) option remember; local k; if n <1 then 1 else 1 + add(2^r*binomial(n,r)*A080253(n-r),r=1..n); fi; end; seq(A080253(n),n=0..30); # Detlef Pauly
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t[n_] := Sum[StirlingS2[n, k] k!, {k, 0, n}]; c[n_] := Sum[Binomial[n, k] 2^k t[k], {k, 0, n}]; Table[c[n], {n, 0, 100}] (* Emanuele Munarini, Oct 04 2012 *)
CoefficientList[Series[E^x/(2-E^(2*x)), {x, 0, 20}], x] * Range[0, 20]! (* Vaclav Kotesovec, Feb 07 2015 *)
Round@Table[(-1)^(n + 1) (PolyLog[-n, Sqrt[2]] - PolyLog[-n, -Sqrt[2]])/(2 Sqrt[2]), {n, 0, 20}] (* Vladimir Reshetnikov, Oct 31 2015 *)
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t(n):=sum(stirling2(n,k)*k!,k,0,n);
c(n):=sum(binomial(n,k)*2^k*t(k),k,0,n);
makelist(c(n),n,0,40); // Emanuele Munarini, Oct 04 2012
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def A080253(n):
return add(A060187(n, k) << (n-k) for k in (0..n))
[A080253(n) for n in (0..17)] # Peter Luschny, Apr 26 2013
More terms from Antonio G. Astudillo (afg_astudillo(AT)hotmail.com), Feb 14 2003
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