A392120 - OEIS

%I #8 Jan 23 2026 13:57:21

%S 2,6,8,9,10,11,14,15,17,18,19,20,21,23,27,30,31,33,34,35,37,38,40,41,

%T 43,46,47,49,51,53,54,55,57,60,67,70,72,77,80,82,84,90,91,95,97,99,

%U 101,108,109,110,111,114,116,118,119,120,121,122,125,127,128,131

%N Numbers k such that (k^3 - greatest prime < k^3) < (-k^3 + least prime > k^3).

%C 3-way partition of integers:

%C   A392120 = s(1) = (2, 6, 8, 9, 10, 11, 14, 15, 17, 18, 19, 20, 21, 23, 27, 30, 31, 33, ...)

%C   A075191 = s(2) = (4, 12, 16, 26, 28, 36, 48, 58, 66, 68, 74, 78, 102, 106, 112, 117, ...)

%C   A392122 = s(3) = (1, 3, 5, 7, 13, 22, 24, 25, 29, 32, 39, 42, 44, 45, 50, 52, 56, 59, ...)

%C The primes indexed by s(1), s(2), s(3) are partitioned into three sequences as follows:

%C   prime(s(1)) = (3, 13, 19, 23, 29, 31, 43, 47, 59, 61, 67, 71, 73, 83, 103, 113, 127, ...)

%C   prime(s(2)) = (7, 37, 53, 101, 107, 151, 223, 271, 317, 337, 373, 397, 557, 577, ...)

%C   prime(s(3)) = (2, 5, 11, 17, 41, 79, 89, 97, 109, 131, 167, 181, 193, 197, 229, 239, ...)

%t z = 600; f[x_] := f[x] = x^3;

%t u[n_] := NextPrime[f[n], -1]; v[n_] := NextPrime[f[n]];

%t s1 = Select[Range[z], f[#] - v[#] < u[#] - f[#] &]   (* A392120 *)

%t s2 = Select[Range[z], f[#] - v[#] == u[#] - f[#] &]  (* A075191 *)

%t s3 = Select[Range[z], f[#] - v[#] > u[#] - f[#] &]   (* A392122 *)

%Y Cf. A390788, A075191, A392122.

%K nonn

%O 1,1

%A _Clark Kimberling_, Jan 18 2026