A308058 Lexicographically earliest sequence of positive terms such that for any distinct m and n, a(m) * a(m+1)^2 <> a(n) * a(n+1)^2.

1, 1, 2, 1, 3, 1, 4, 3, 2, 2, 3, 3, 4, 4, 5, 1, 5, 2, 4, 6, 1, 7, 1, 9, 5, 3, 5, 4, 7, 2, 5, 5, 6, 2, 6, 3, 6, 4, 8, 4, 9, 7, 3, 7, 4, 10, 1, 11, 1, 13, 1, 17, 1, 19, 1, 22, 1, 23, 1, 24, 3, 8, 5, 7, 5, 8, 6, 5, 9, 9, 10, 2, 7, 6, 7, 7, 8, 7, 9, 11, 2, 9, 12

Offset: 1

Author

Rémy Sigrist, May 10 2019

Keywords

• nonn

Comments

This sequence has similarities with A088178; here we consider a(n)*a(n+1)^2, there we consider a(n)*a(n+1).

Examples

			The first terms, alongside a(n)*a(n+1)^2, are:
  n   a(n)  a(n)*a(n+1)^2
  --  ----  -------------
   1     1              1
   2     1              4
   3     2              2
   4     1              9
   5     3              3
   6     1             16
   7     4             36
   8     3             12
   9     2              8
  10     2             18
		

Links

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

Crossrefs

See A308057 for an additive variant.

Cf. A088178.

Programs

PARI

s=0; v=1; for(n=1, 83, print1(v", "); for (w=1, oo, if (!bittest(s,x=v*w^2), s+=2^x; v=w; break)))