A286763 - OEIS

%I #26 Sep 10 2024 08:16:06

%S 1,30,210,330,2310,3990,6090,14790,43890,66990,82110,125970,144210,

%T 181830,881790,1009470,1067430,1217370,2284590,2381190,17687670,

%U 18888870,26265030,35068110,39544890,47763870,115223790,127652070,406816410,497668710,741110370,1024748670

%N Numbers that appear in A195441 at least once for two consecutive indices.

%C 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

%H Bernd C. Kellner, <a href="https://doi.org/10.1016/j.jnt.2017.03.020">On a product of certain primes</a>, J. Number Theory 179 (2017), 126-141; arXiv:<a href="https://arxiv.org/abs/1705.04303">1705.04303</a> [math.NT], 2017.

%H Bernd C. Kellner and Jonathan Sondow, <a href="https://doi.org/10.4169/amer.math.monthly.124.8.695">Power-Sum Denominators</a>, Amer. Math. Monthly 124 (2017), 695-709; arXiv:<a href="https://arxiv.org/abs/1705.03857">1705.03857</a> [math.NT], 2017.

%H Bernd C. Kellner and Jonathan Sondow, <a href="https://doi.org/10.5281/zenodo.10682734">The denominators of power sums of arithmetic progressions</a>, Integers 18 (2018), Article #A95, 17 pp.; arXiv:<a href="https://arxiv.org/abs/1705.05331">1705.05331</a> [math.NT], 2017.

%e A195441(21) = A195441(22) = 30, so 30 is in the sequence. - _Jonathan Sondow_, Dec 11 2018

%t 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 *)

%o (Julia)

%o function A286763_search()

%o     A = fmpz[]; a = fmpz(0)

%o     for n in 0:10000

%o         u = A195441(n)

%o         a == u && push!(A, a)

%o         a = u

%o     end

%o     S = sort([a for a in Set(A)])

%o S[1:32] end

%o println(A286763_search())

%Y Cf. A195441, A286516, A286762.

%K nonn

%O 1,2

%A _Peter Luschny_, May 14 2017