A334857 Lexicographically earliest sequence of integers > 1 such that for any distinct m and n, a(m)^a(m+1) <> a(n)^a(n+1).

2, 2, 3, 2, 4, 3, 3, 4, 4, 5, 2, 5, 3, 5, 4, 6, 2, 7, 2, 9, 3, 7, 3, 8, 5, 5, 6, 3, 9, 5, 7, 4, 7, 5, 8, 6, 4, 8, 7, 6, 5, 9, 6, 6, 7, 7, 8, 8, 9, 7, 9, 8, 10, 2, 11, 2, 13, 2, 17, 2, 19, 2, 20, 2, 22, 2, 23, 2, 25, 5, 11, 3, 11, 4, 13, 3, 13, 4, 14, 2, 29, 2

Offset: 1

Author

Rémy Sigrist, May 13 2020

Keywords

• nonn

Comments

This sequence has similarities with A088177; here we raise consecutive terms, there we multiply consecutive terms.

This sequence contains large runs of consecutive terms where every other term equals 2.

Examples

			The first terms, alongside a(n)^a(n+1), are:
  n   a(n)  a(n)^a(n+1)
  --  ----  -----------
   1     2            4
   2     2            8
   3     3            9
   4     2           16
   5     4           64
   6     3           27
   7     3           81
   8     4          256
   9     4         1024
  10     5           25
  11     2           32
  12     5          125
  13     3          243
		

Links

• Rémy Sigrist, Table of n, a(n) for n = 1..10000
• Rémy Sigrist, PARI program for A334857

Crossrefs

Cf. A088177, A334858.

Programs

PARI

See Links section.