A376244 Lexicographically earliest sequence of positive integers a(1), a(2), ... with the property that the lexicographically earliest sequence of positive integers b(1), b(2), ... such that for any n > 0, S(n) = Sum_{k = 1..n} 1 / (a(k)*b(k)) < 1, also implies that S(n) is never of the form (e_n - 1) / e_n for some integer e_n.

3, 4, 5, 4, 7, 3, 9, 1, 11, 4, 13, 7, 9, 19, 10, 2, 23, 25, 29, 27, 53, 1, 17, 7, 2, 2, 15, 67, 22, 37

Offset: 1

Author

Rémy Sigrist and N. J. A. Sloane, Sep 16 2024

Keywords

• nonn
• more

Comments

Is this sequence infinite?

Examples

			The initial terms are:
  n  a(n)  b(n)    S(n)
  -  ----  ------  ---------------------------
  1     3       1  1/3
  2     4       1  7/12
  3     5       1  47/60
  4     4       2  109/120
  5     7       2  823/840
  6     3      17  4757/4760
  7     9     177  7582661/7582680
  8     1  399089  3026164178509/3026164178520
		

Links

• Rémy Sigrist, PARI program

Crossrefs

Cf. A374663, A376062, A376184, A376245 (corresponding b's), A376246-A376247 (numerator and denominator of corresponding S(n)).

Programs

PARI

\\ See Links section.