A390785 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.

2, 9, 30, 146, 99, 263, 429, 650, 217, 1879, 1831, 3077, 2225, 4260, 3644, 8688, 12542, 3385, 17006, 23283, 14357, 44903, 34215, 30802, 33608, 106286, 85633, 31545, 103520, 141718, 126172, 141334, 104071, 436612, 271743, 786922, 149689, 325852, 1150400

Offset

1,1

Comments

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, ...).

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)":

m = 2: A038664

m = 3: A213903

m = 4: this sequence

m = 5: A390786

m = 6: A390787

Links

Table of n, a(n) for n=1..39.

Example

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

Mathematica

p[n_] := p[n] = Prime[n]; m = 4; z = 60000;
t = Table[Floor[p[n + 1]/m] - Floor[p[n]/m], {n, 1, z}];
Flatten[Table[First[Position[t, k]], {k, 1, 20}]]

Crossrefs

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

Sequence in context: A389325 A181954 A343565 * A318101 A358652 A347893

Adjacent sequences: A390782 A390783 A390784 * A390786 A390787 A390788

Keyword

nonn

Author

Clark Kimberling, Nov 24 2025

Status

approved