A376246 -id:A376246 - cp's OEIS frontend

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

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

Is this sequence infinite?

			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

Rémy Sigrist, PARI program

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

PARI
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A376245 Lexicographically earliest sequence of positive integers a(1), a(2), ... such that for any n > 0, Sum_{k = 1..n} 1 / (a(k) * A376244(k)) < 1.

Original entry on oeis.org

1, 1, 1, 2, 2, 17, 177, 399089, 25009621311, 1875034732942983344228, 1539443127106211836190570031058344660910551, 4678021254342525951806601314996862405949898779699686841158030172103896860849760557451

Offset: 1

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

nonn

Rémy Sigrist, PARI program

Cf. A376244, A376246, A376247.

PARI
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A376247 a(n) is the denominator of Sum_{k = 1..n} 1 / (A376244(k) * A376245(k)).

Original entry on oeis.org

3, 12, 60, 120, 840, 4760, 7582680, 3026164178520, 277505140475561534945640, 260165888480949800316206335248860247693882960, 1735545885361077128120249087863835952607412447268583818069629193850545735375261166814160

Offset: 1

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

Rémy Sigrist, PARI program

Cf. A376244, A376245, A376246.

PARI
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\\ See Links section.
```

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A376245 Lexicographically earliest sequence of positive integers a(1), a(2), ... such that for any n > 0, Sum_{k = 1..n} 1 / (a(k) * A376244(k)) < 1.

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PARI

A376247 a(n) is the denominator of Sum_{k = 1..n} 1 / (A376244(k) * A376245(k)).

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PARI