login

Year-end appeal: Please make a donation to the OEIS Foundation to support ongoing development and maintenance of the OEIS. We are now in our 61st year, we have over 378,000 sequences, and we’ve reached 11,000 citations (which often say “discovered thanks to the OEIS”).

Numbers k such that A173557(k) = A173557(k+1).
2

%I #9 Apr 09 2020 05:24:32

%S 1,168,194,350,1368,1628,3705,5186,5328,6929,7475,25545,26047,26864,

%T 28251,34936,37248,56724,65675,81732,82368,87308,87367,88450,91539,

%U 132308,164691,166624,244215,265524,280818,281897,388245,465651,501024,577524,806895,859901

%N Numbers k such that A173557(k) = A173557(k+1).

%C Kim et al. (2019) conjectured that A173557(k) = A173557(k+1) is divisible by 12 for all the terms k > 1.

%H Amiram Eldar, <a href="/A333874/b333874.txt">Table of n, a(n) for n = 1..712</a> (terms below 2*10^10)

%H Daeyeoul Kim, Umit Sarp, and Sebahattin Ikikardes, <a href="http://dx.doi.org/10.18514/MMN.2019.2470">Certain combinatoric convolution sums arising from Bernoulli and Euler Polynomials</a>, Miskolc Mathematical Notes, No. 20, Vol. 1 (2019): pp. 311-330.

%e 1 is a term since A173557(1) = A173557(2) = 1.

%t f[p_, e_] := p - 1; u[1] = 1; u[n_] := Times @@ (f @@@ FactorInteger[n]); s = {}; u1 = 1; Do[u2 = u[n]; If[u1 == u2, AppendTo[s, n-1]]; u1 = u2, {n, 2, 10^5}]; s

%Y Cf. A001274, A173557, A333875.

%K nonn

%O 1,2

%A _Amiram Eldar_, Apr 08 2020