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A272139
Numbers n such that Bernoulli number B_{n} has denominator 1806.
27
42, 294, 798, 1806, 2058, 2814, 2982, 4074, 4578, 5334, 5586, 6594, 6846, 8106, 8274, 8358, 9366, 9534, 12642, 12894, 13314, 14154, 14658, 15162, 17178, 18186, 19194, 20118, 20454, 21882, 21966, 22722, 22974, 23982, 25914, 26502, 27006, 28266, 28518, 29778
OFFSET
1,1
COMMENTS
1806 = 2 * 3 * 7 * 43.
All terms are multiple of a(1) = 42.
For these numbers numerator(B_{n}) mod denominator(B_{n}) = 1.
In 2005, B. C. Kellner proved E. W. Weisstein's conjecture that denom(B_n) = n only if n = 1806.
LINKS
EXAMPLE
Bernoulli B_{42} is 1520097643918070802691/1806, hence 42 is in the sequence.
MAPLE
with(numtheory): P:=proc(q, h) local n; for n from 2 by 2 to q do
if denom(bernoulli(n))=h then print(n); fi; od; end: P(10^6, 1806);
MATHEMATICA
Select[Range[0, 1000], Denominator[BernoulliB[#]] == 1806 &] (* Robert Price, Apr 21 2016 *)
Select[Range[42, 30000, 42], Denominator[BernoulliB[#]]==1806&] (* Harvey P. Dale, Jun 01 2019 *)
PROG
(PARI) lista(nn) = for(n=1, nn, if(denominator(bernfrac(n)) == 1806, print1(n, ", "))); \\ Altug Alkan, Apr 22 2016
KEYWORD
nonn
AUTHOR
Paolo P. Lava, Apr 21 2016
EXTENSIONS
More terms from Altug Alkan, Apr 22 2016
STATUS
approved