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

1,2

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

Table of n, a(n) for n=1..32.

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

Cf. A195441, A286516, A286762.

Sequence in context: A181629 A346245 A129499 * A347828 A069965 A215627

Adjacent sequences: A286760 A286761 A286762 * A286764 A286765 A286766

Keyword

nonn,changed

Author

Peter Luschny, May 14 2017

Status

approved