A390785 - OEIS

%I #12 Dec 01 2025 21:09:19

%S 2,9,30,146,99,263,429,650,217,1879,1831,3077,2225,4260,3644,8688,

%T 12542,3385,17006,23283,14357,44903,34215,30802,33608,106286,85633,

%U 31545,103520,141718,126172,141334,104071,436612,271743,786922,149689,325852,1150400

%N a(n) is the least k such that the number of integers between (1/4)*prime(k) and (1/4)*prime(k+1) is n.

%C The sequence of primes indexed by this sequence is (3, 23, 113, 839, 523, 1669, 2971, 4831, 1327, 16141, 15683, 28229, 19609, 40639, 34061, 89689, ...).

%C Guide to sequences defined by "n-th number k such that there is an integer between (1/m)*prime(n) and (1/m)*prime(n+1)":

%C m = 2: A038664

%C m = 3: A213903

%C m = 4: this sequence

%C m = 5: A390786

%C m = 6: A390787

%e 3/4 < 1 < 5/4 and 0 < 2/4 < 3/4 < 1, so a(1) = 2.

%t p[n_] := p[n] = Prime[n]; m = 4; z = 60000;

%t t = Table[Floor[p[n + 1]/m] - Floor[p[n]/m], {n, 1, z}];

%t Flatten[Table[First[Position[t, k]], {k, 1, 20}]]

%Y Cf. A000027, A000040, A390786, A390787, A390788.

%K nonn

%O 1,1

%A _Clark Kimberling_, Nov 24 2025