VOOZH about

URL: https://oeis.org/A392120

⇱ A392120 - OEIS


login
A392120
Numbers k such that (k^3 - greatest prime < k^3) < (-k^3 + least prime > k^3).
3
2, 6, 8, 9, 10, 11, 14, 15, 17, 18, 19, 20, 21, 23, 27, 30, 31, 33, 34, 35, 37, 38, 40, 41, 43, 46, 47, 49, 51, 53, 54, 55, 57, 60, 67, 70, 72, 77, 80, 82, 84, 90, 91, 95, 97, 99, 101, 108, 109, 110, 111, 114, 116, 118, 119, 120, 121, 122, 125, 127, 128, 131
OFFSET
1,1
COMMENTS
3-way partition of integers:
A392120 = s(1) = (2, 6, 8, 9, 10, 11, 14, 15, 17, 18, 19, 20, 21, 23, 27, 30, 31, 33, ...)
A075191 = s(2) = (4, 12, 16, 26, 28, 36, 48, 58, 66, 68, 74, 78, 102, 106, 112, 117, ...)
A392122 = s(3) = (1, 3, 5, 7, 13, 22, 24, 25, 29, 32, 39, 42, 44, 45, 50, 52, 56, 59, ...)
The primes indexed by s(1), s(2), s(3) are partitioned into three sequences as follows:
prime(s(1)) = (3, 13, 19, 23, 29, 31, 43, 47, 59, 61, 67, 71, 73, 83, 103, 113, 127, ...)
prime(s(2)) = (7, 37, 53, 101, 107, 151, 223, 271, 317, 337, 373, 397, 557, 577, ...)
prime(s(3)) = (2, 5, 11, 17, 41, 79, 89, 97, 109, 131, 167, 181, 193, 197, 229, 239, ...)
MATHEMATICA
z = 600; f[x_] := f[x] = x^3;
u[n_] := NextPrime[f[n], -1]; v[n_] := NextPrime[f[n]];
s1 = Select[Range[z], f[#] - v[#] < u[#] - f[#] &] (* A392120 *)
s2 = Select[Range[z], f[#] - v[#] == u[#] - f[#] &] (* A075191 *)
s3 = Select[Range[z], f[#] - v[#] > u[#] - f[#] &] (* A392122 *)
CROSSREFS
KEYWORD
nonn
AUTHOR
Clark Kimberling, Jan 18 2026
STATUS
approved