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Numbers k such that 4*k - (greatest prime < 4*k) = (least prime > 4*k) - 4*k.
4

%I #6 Dec 28 2025 16:05:55

%S 1,3,14,15,16,18,19,27,30,36,40,44,45,48,57,59,60,65,72,75,78,81,87,

%T 89,94,105,108,109,133,136,138,140,149,150,151,159,164,165,170,174,

%U 184,195,198,204,207,231,236,240,245,254,255,258,259,261,264,273,275

%N Numbers k such that 4*k - (greatest prime < 4*k) = (least prime > 4*k) - 4*k.

%t z = 1500; f[x_] := f[x] = 4*x;

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

%t Select[Range[400], m*# - v[#] < u[#] - m*# &] (* A391354 *)

%t Select[Range[400], m*# - v[#] == u[#] - m*# &] (* A391355 *)

%t Select[Range[400], m*# - v[#] > u[#] - m*# &] (* A391356 *)

%Y Cf. A000027, A000040, A391351, A391354, A391356.

%K nonn

%O 1,2

%A _Clark Kimberling_, Dec 14 2025