A385174 Indices k such that P(k-1) < Q(n) <= P(k), where primorial P = A002110 and superprimorial Q = A006939.

0, 1, 2, 4, 6, 8, 11, 15, 19, 23, 28, 33, 39, 46, 52, 60, 68, 76, 85, 94, 104, 114, 125, 136, 148, 160, 173, 186, 200, 215, 229, 245, 260, 277, 294, 311, 329, 347, 366, 385, 405, 426, 446, 468, 490, 512, 535, 558, 582, 607, 632, 657, 683, 709, 736, 764, 792, 820

Offset

0,3

Links

Michael De Vlieger, Table of n, a(n) for n = 0..2000

Example

a(0) = 0 since P(0) = Q(0) = 1.
a(1) = 1 since P(1) = Q(1) = 2.
a(2) = 2 since P(2) < Q(2) < P(3), i.e., 6 < 12 < 30.
a(3) = 4 since P(4) < Q(3) < P(5), i.e., 210 < 360 < 2310.
a(4) = 6 since P(6) < Q(4) < P(7), i.e., 30030 < 75600 < 510510.
a(5) = 8 since P(8) < Q(5) < P(9), i.e., 9699690 < 174636000 < 223092870, etc.

Mathematica

f[x_] := Times @@ Flatten@ MapIndexed[Prime[#2]^#1 &, x]; j = 0; P = 1; {0}~Join~Table[Set[k, f[Range[n, 1, -1]]]; While[P <= k, j++; P *= Prime[j] ]; j -1, {n, 57}]

Crossrefs

Cf. A000040, A002110, A006939.

Sequence in context: A213609 A374263 A338237 * A393465 A039823 A284617

Adjacent sequences: A385171 A385172 A385173 * A385175 A385176 A385177

Keyword

nonn

Author

Michael De Vlieger, Sep 16 2025

Status

approved