|
|
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
(list;
graph;
refs;
listen;
history;
text;
internal format)
|
|
|
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
|
|
CROSSREFS
|
Cf. A045979, A051222, A051225, A051226, A051227, A051228, A051229, A051230, A119456, A119480, A249134, A255684, A271634, A271635, A272138, A272140, A272183, A272184, A272185, A272186.
|
|
KEYWORD
|
nonn
|
|
AUTHOR
|
|
|
EXTENSIONS
|
|
|
STATUS
|
approved
|
|
|
|