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

%I #5 Dec 20 2025 13:29:04

%S 4,7,9,10,13,22,24,25,28,31,34,37,39,43,47,49,52,55,58,62,64,67,69,70,

%T 73,76,79,82,84,86,88,91,93,97,99,100,102,104,107,112,114,115,119,121,

%U 124,127,129,130,134,135,139,142,144,146,148,153,154,157,160

%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, A391355.

%K nonn

%O 1,1

%A _Clark Kimberling_, Dec 18 2025