A272139 - OEIS

%I #30 Jun 01 2019 11:31:35

%S 42,294,798,1806,2058,2814,2982,4074,4578,5334,5586,6594,6846,8106,

%T 8274,8358,9366,9534,12642,12894,13314,14154,14658,15162,17178,18186,

%U 19194,20118,20454,21882,21966,22722,22974,23982,25914,26502,27006,28266,28518,29778

%N Numbers n such that Bernoulli number B_{n} has denominator 1806.

%C 1806 = 2 * 3 * 7 * 43.

%C All terms are multiple of a(1) = 42.

%C For these numbers numerator(B_{n}) mod denominator(B_{n}) = 1.

%C In 2005, B. C. Kellner proved E. W. Weisstein's conjecture that denom(B_n) = n only if n = 1806.

%H Seiichi Manyama, <a href="/A272139/b272139.txt">Table of n, a(n) for n = 1..1000</a>

%e Bernoulli B_{42} is 1520097643918070802691/1806, hence 42 is in the sequence.

%p with(numtheory): P:=proc(q,h) local n;  for n from 2 by 2 to q do

%p if denom(bernoulli(n))=h then print(n); fi; od; end: P(10^6,1806);

%t Select[Range[0, 1000], Denominator[BernoulliB[#]] == 1806 &] (* _Robert Price_, Apr 21 2016 *)

%t Select[Range[42,30000,42],Denominator[BernoulliB[#]]==1806&] (* _Harvey P. Dale_, Jun 01 2019 *)

%o (PARI) lista(nn) = for(n=1, nn, if(denominator(bernfrac(n)) == 1806, print1(n, ", "))); \\ _Altug Alkan_, Apr 22 2016

%Y Cf. A045979, A051222, A051225, A051226, A051227, A051228, A051229, A051230, A119456, A119480, A249134, A255684, A271634, A271635, A272138,  A272140, A272183, A272184, A272185, A272186.

%K nonn

%O 1,1

%A _Paolo P. Lava_, Apr 21 2016

%E More terms from _Altug Alkan_, Apr 22 2016