A333559 Lexicographically earliest infinite sequence of positive terms such that for any two distinct nonempty intervals, say [t, u] and [v, w], a(t) * ... * a(u) <> a(v) * ... * a(w).

2, 3, 4, 5, 7, 8, 9, 10, 11, 13, 14, 15, 17, 16, 18, 19, 21, 22, 23, 25, 26, 27, 28, 29, 30, 31, 32, 33, 34, 36, 37, 38, 39, 40, 41, 42, 43, 44, 45, 46, 47, 48, 49, 50, 51, 52, 53, 54, 55, 57, 58, 59, 61, 62, 63, 64, 65, 66, 67, 68, 69, 70, 71, 73, 74, 75, 76

Offset

1,1

Comments

By necessity, all terms are distinct and strictly greater than 1.

This sequence is a variant of A101274.

Does every positive integer correspond to a product of consecutive terms?

Links

Table of n, a(n) for n=1..67.

Rémy Sigrist, PARI program for A333559

Formula

a(n) = A079854(n+2) / A079854(n+1).

Example

The values of a(i) * ... * a(j) for i <= j <= 7 are:
  i\j|  1  2   3    4    5     6      7
  ---+---------------------------------
    1|  2  6  24  120  840  6720  60480
    2|  .  3  12   60  420  3360  30240
    3|  .  .   4   20  140  1120  10080
    4|  .  .   .    5   35   280   2520
    5|  .  .   .    .    7    56    504
    6|  .  .   .    .    .     8     72
    7|  .  .   .    .    .     .      9

Prog

(PARI) See Links section.

Crossrefs

Cf. A079854, A101274 (additive variant), A333555 (XOR variant).

Sequence in context: A049093 A098901 A098767 * A153381 A307750 A356734

Adjacent sequences: A333556 A333557 A333558 * A333560 A333561 A333562

Keyword

nonn

Author

Rémy Sigrist, Mar 26 2020

Status

approved