A390787 a(n) is the least k such that there are exactly n integers between (1/6)*prime(k) and (1/6)*prime(k+1).

3, 24, 30, 154, 217, 738, 1879, 1831, 3427, 4522, 3644, 3385, 17006, 38590, 14357, 30802, 49414, 31545, 40933, 141718, 126172, 104071, 271743, 149689, 325852, 566214, 2386432, 1287544, 1736516, 1094421, 2219883, 4140009, 2775456

Offset

1,1

Comments

The sequence of primes indexed by this sequence is (5, 89, 113, 887, 1327, 5591, 16141, 15683, 31907, 43331, 34061, 31397, 188029, 461717, 155921, ...). See A390785 for a guide to related sequences.

Links

Table of n, a(n) for n=1..33.

Formula

floor(prime(a(n)+1)/6) - floor(prime(a(n))/6) = n.

Maple

N:= 40: # for a(1) .. a(N)
V:= Vector(N): p:= 2: m:= 0: count:= 0:
for k from 1 while count < N do
  p:= nextprime(p); mp:= floor(p/6);
  v:= mp - m; m:= mp;
  if v > 0 and v <= N and V[v] = 0 then
    V[v]:= k; count:= count+1;
  fi;
od:
convert(V, list); # Robert Israel, Nov 25 2025

Mathematica

p[n_] := p[n] = Prime[n]; m = 6; z = 50000;
t = Table[Floor[p[n + 1]/m] - Floor[p[n]/m], {n, 1, z}];
Flatten[Table[First[Position[t, k]], {k, 1, 40}]]

Crossrefs

Cf. A390785, A390786, A390788.

Sequence in context: A081312 A123598 A106217 * A267274 A217554 A278491

Adjacent sequences: A390784 A390785 A390786 * A390788 A390789 A390790

Keyword

nonn

Author

Clark Kimberling, Nov 24 2025

Status

approved