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A051228 Bernoulli number B_{n} has denominator 42. 28
6, 114, 186, 258, 354, 402, 426, 474, 582, 654, 762, 834, 894, 942, 978, 1002, 1158, 1182, 1194, 1266, 1338, 1362, 1374, 1614, 1842, 1902, 2022, 2094, 2118, 2166, 2274, 2298, 2334, 2406, 2454, 2526, 2598, 2634, 2694, 2742, 2778, 2874, 2922, 2994, 3126 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,1

COMMENTS

From the von Staudt-Clausen theorem, denominator(B_2n) = product of primes p such that (p-1)|2n.

Numerator(B_{n}) mod Denominator(B_{n}) = 1. This relation stands also for B_{n} with denominator equal to 1, 2, 6 and 1806 (A014117). - Paolo P. Lava, Mar 07 2017

REFERENCES

B. C. Berndt, Ramanujan's Notebooks Part IV, Springer-Verlag, see p. 75.

LINKS

T. D. Noe, Table of n, a(n) for n = 1..1000

Index entries for sequences related to Bernoulli numbers.

MATHEMATICA

2*Select[Range[2000], Denominator[BernoulliB[2#]] == 42 &](* Jean-Fran├žois Alcover, Nov 25 2011 *)

Position[BernoulliB[Range[3200]], _?(Denominator[#]==42&)]//Flatten (* Harvey P. Dale, Jul 02 2018 *)

PROG

(Perl) @p=(2, 3, 5, 7); @c=(4); $p=7; for($n=6; $n<=3126; $n+=6){while($p<$n+1){$p+=2; next if grep$p%$_==0, @p; push@p, $p; push@c, $p-1; }print"$n, "if!grep$n%$_==0, @c; }print"\n"

(PARI) is(n)=denominator(bernfrac(n))==42 \\ Charles R Greathouse IV, Feb 07 2017

CROSSREFS

Cf. A045979, A051222, A051225-A051230.

Sequence in context: A288561 A291917 A066931 * A194132 A194476 A059116

Adjacent sequences:  A051225 A051226 A051227 * A051229 A051230 A051231

KEYWORD

nonn,nice,easy

AUTHOR

N. J. A. Sloane

EXTENSIONS

More terms and Perl program from Hugo van der Sanden

STATUS

approved

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Last modified March 22 01:06 EDT 2019. Contains 321406 sequences. (Running on oeis4.)