A334390 Lexicographically earliest sequence of distinct positive integers such that for any n > 0, a(n), a(2*n) and a(2*n+1) are in geometric progression.

1, 2, 4, 6, 18, 8, 16, 12, 24, 30, 50, 28, 98, 20, 25, 36, 108, 48, 96, 60, 120, 40, 32, 14, 7, 84, 72, 10, 5, 15, 9, 42, 49, 54, 27, 132, 363, 144, 216, 90, 135, 180, 270, 80, 160, 64, 128, 56, 224, 21, 63, 126, 189, 156, 338, 70, 490, 35, 245, 75, 375, 33

Offset

1,2

Comments

This sequence is a variant of A305410; here we consider geometric progressions, there arithmetic progressions.

Links

Rémy Sigrist, Table of n, a(n) for n = 1..6667

Rémy Sigrist, PARI program for A334390

Example

The first terms, alongside the corresponding common ratios, are:
  n   a(n)  a(2*n)  a(2*n+1)  r
  --  ----  ------  --------  ---
   1     1       2         4    2
   2     2       6        18    3
   3     4       8        16    2
   4     6      12        24    2
   5    18      30        50  5/3
   6     8      28        98  7/2
   7    16      20        25  5/4
   8    12      36       108    3
   9    24      48        96    2
  10    30      60       120    2

Prog

(PARI) See Links section.

Crossrefs

Cf. A305410, A334384.

Sequence in context: A294920 A046441 A192335 * A067993 A074131 A355078

Adjacent sequences: A334387 A334388 A334389 * A334391 A334392 A334393

Keyword

nonn

Author

Rémy Sigrist, Apr 26 2020

Status

approved