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Numbers k such that A014085(k) = A014085(k+1).
3

%I #14 Feb 23 2020 07:11:37

%S 1,2,12,18,20,21,29,36,59,66,71,73,88,90,94,95,103,104,109,128,130,

%T 131,161,166,170,209,234,250,292,299,307,318,332,353,362,375,377,391,

%U 481,509,556,557,564,577,602,619,630,665,670,684,698,728,792,808,840

%N Numbers k such that A014085(k) = A014085(k+1).

%C Numbers k such that number of primes between k^2 and (k+1)^2 is equal to number of primes between (k+1)^2 and (k+2)^2.

%C Conjecture: the sequence is infinite.

%H Zak Seidov and Amiram Eldar, <a href="/A144264/b144264.txt">Table of n, a(n) for n = 1..3000</a> (terms 1..2000 from Zak Seidov)

%t Flatten[Position[Partition[PrimePi[Range[1000]^2],3,1],_?(Length[Union[ Differences[#]]]==1&),{1},Heads->False]] (* _Harvey P. Dale_, Jun 17 2014 *)

%Y Cf. A014085, A144359.

%K nonn

%O 1,2

%A _Zak Seidov_, Sep 16 2008, Sep 17 2008