

A119864


Numbers n such that the numerator of BernoulliB[n] is divisible by 691.


1



12, 200, 702, 890, 1382, 1392, 1580, 2082, 2270, 2764, 2772, 2960, 3462, 3650, 4146, 4152, 4340, 4842, 5030, 5528, 5532, 5720, 6222, 6410, 6910, 6912, 7100, 7602, 7790, 8292, 8480, 8982, 9170, 9672, 9674, 9860, 10362, 10550, 11052, 11056, 11240, 11742
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OFFSET

1,1


COMMENTS

a(n) is a union of 3 arithmetic progressions: 12 + 690*n = {12,702,1392,2082,2772,3462,4152,4842,5532,6222,6912,7602,8292,8982,9672,...}, 200 + 690*n = {200,890,1580,2270,2960,3650,4340,5030,5720,6410,7100,7790,8480,9170,9860,...}, 2*691*n = {1382,2764,4146,5528,6910,8292,9674,...}. Note that Numerator[BernoulliB[8292]] is divisible by 691^2, where a(n) = 8292 = 12 + 690*13 = 691*12. It appears that Numerator[BernoulliB[138200]] is also divisible by 691^2 because a(n) = 138200 = 200 + 690*201 = 691*200.


LINKS

Table of n, a(n) for n=1..42.
The Bernoulli Number Page, www.bernoulli.org


FORMULA

Mod[ Numerator[ BernoulliB[ a(n) ]], 691] = 0.


EXAMPLE

BernoulliB[n] sequence begins 1, 1/2, 1/6, 0, 1/30, 0, 1/42, 0, 1/30, 0, 5/66, 0, 691/2730, 0, 7/6, 0, 3617/510, ...
a(1) = 12 because Numerator[BernoulliB[12]] = 691.


MATHEMATICA

Select[Union[Table[2n*691, {n, 1, 30}], Table[12+690*n, {n, 0, 30}], Table[200+690*n, {n, 0, 30}]], #<=20000&]
Select[Range[2, 12000, 2], Divisible[Numerator[BernoulliB[#]], 691]&] (* Harvey P. Dale, Nov 19 2014 *)


CROSSREFS

Cf. A027641.
Sequence in context: A115865 A291285 A159359 * A036240 A292056 A277311
Adjacent sequences: A119861 A119862 A119863 * A119865 A119866 A119867


KEYWORD

nonn


AUTHOR

Alexander Adamchuk, Jul 31 2006


STATUS

approved



