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Search: id:A132184
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| A132184 |
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Numbers n such that the numerator of the Bernoulli number B(2n) ends with the digits 691. |
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+0
1
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| 6, 21, 27, 321, 1266, 1527, 1821, 2526, 2576, 2721, 2950, 3126, 3246, 3426, 4206, 4236, 4821, 4926, 5286, 5721, 5946, 5950, 6100, 6351, 7018, 7138, 7172, 7386, 7806, 7931, 8037, 8790, 8796, 8826, 9021, 9048, 9426, 9478, 9726, 9921, 10221, 10326
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OFFSET
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1,1
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COMMENT
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The numerator of BernoulliB(12) is 691. The sequence gives a semi-indices of the 691-automorphic numerators in the BernoulliB(n) sequence. All 4 initial terms are the multiples of 3. Note that Bernoulli numerators corresponding to the first two terms are the automorphic primes: 691 and 1520097643918070802691.
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LINKS
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Eric Weisstein's World of Mathematics, Bernoulli Number.
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EXAMPLE
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a(1) = 6 because BernoulliB(2*6) = - 691/2730.
a(2) = 21 because BernoulliB(2*21) = 1520097643918070802691/1806.
a(3) = 27 because BernoulliB(2*27) = 29149963634884862421418123812691/798.
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MATHEMATICA
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Do[ g=Numerator[ BernoulliB[ 2n ] ]; f=Mod[ Abs[ g ], 1000 ]; If[ f==691, Print[ n ] ], {n, 1, 1000}]
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CROSSREFS
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Cf. A000367 = Numerators of Bernoulli numbers B_2n. Cf. A092132 = Indices n of Bernoulli numbers B(n) whose numerators are primes. Cf. A092133 = Prime numerators of Bernoulli numbers.
Sequence in context: A143416 A020880 A046467 this_sequence A143322 A034897 A064440
Adjacent sequences: A132181 A132182 A132183 this_sequence A132185 A132186 A132187
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KEYWORD
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base,nonn
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AUTHOR
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Alexander Adamchuk (alex(AT)kolmogorov.com), Nov 04 2007
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EXTENSIONS
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a(5)-a(42) from Donovan Johnson (donovan.johnson(AT)yahoo.com), Sep 05 2008
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