A286763 Numbers that appear in A195441 at least once for two consecutive indices.

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

Author

Peter Luschny, May 14 2017

Keywords

• nonn

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

Examples

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

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.

Crossrefs

Cf. A195441, A286516, A286762.

Programs

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())

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 *)