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A286763
Numbers that appear in A195441 at least once for two consecutive indices.
5
1, 30, 210, 330, 2310, 3990, 6090, 14790, 43890, 66990, 82110, 125970, 144210, 181830, 881790, 1009470, 1067430, 1217370, 2284590, 2381190, 17687670, 18888870, 26265030, 35068110, 39544890, 47763870, 115223790, 127652070, 406816410, 497668710, 741110370, 1024748670
OFFSET
1,2
COMMENTS
The sequence is infinite; see Cor. 3 in "The denominators of power sums of arithmetic progressions". - Bernd C. Kellner and Jonathan Sondow, May 24 2017
LINKS
Bernd C. Kellner, On a product of certain primes, J. Number Theory 179 (2017), 126-141; arXiv:1705.04303 [math.NT], 2017.
Bernd C. Kellner and Jonathan Sondow, Power-Sum Denominators, Amer. Math. Monthly 124 (2017), 695-709; arXiv:1705.03857 [math.NT], 2017.
Bernd C. Kellner and Jonathan Sondow, The denominators of power sums of arithmetic progressions, Integers 18 (2018), Article #A95, 17 pp.; arXiv:1705.05331 [math.NT], 2017.
EXAMPLE
A195441(21) = A195441(22) = 30, so 30 is in the sequence. - Jonathan Sondow, Dec 11 2018
MATHEMATICA
Take[#, 32] &@ Union@ SequenceCases[ Table[ Denominator[ Together[ (BernoulliB[n + 1, x] - BernoulliB[n + 1])]], {n, 0, 2000}], w_ /; And[SameQ @@ w, Length@ w >= 2]][[All, 1]] (* Michael De Vlieger, Sep 22 2017, after Jonathan Sondow at A195441 *)
PROG
(Julia)
function A286763_search()
A = fmpz[]; a = fmpz(0)
for n in 0:10000
u = A195441(n)
a == u && push!(A, a)
a = u
end
S = sort([a for a in Set(A)])
S[1:32] end
println(A286763_search())
CROSSREFS
KEYWORD
nonn
AUTHOR
Peter Luschny, May 14 2017
STATUS
approved