A175343 -id:A175343 - cp's OEIS frontend

A375579 Lexicographically earliest sequence of distinct positive integers such that the products of two consecutive terms belong to A055932.

1, 2, 3, 4, 6, 5, 12, 8, 9, 10, 15, 14, 30, 7, 60, 16, 18, 20, 21, 40, 24, 25, 36, 27, 32, 45, 28, 75, 42, 35, 48, 50, 54, 64, 72, 70, 33, 140, 63, 80, 81, 90, 49, 120, 56, 105, 22, 210, 11, 420, 44, 315, 66, 175, 84, 55, 126, 100, 96, 108, 125, 144, 128, 135

Offset: 1

Rémy Sigrist, Aug 19 2024

nonn

a(n+1) is a multiple of A083720(a(n)).

This sequence has similarities with A175343; here we consider prime factors of consecutive terms, there ones in binary expansions of consecutive terms.

			The first terms, alongside their prime factors, are:
  n   a(n)  2  3  5  7
  --  ----  -  -  -  -
   1     1
   2     2  X
   3     3     X
   4     4  X
   5     6  X  X
   6     5        X
   7    12  X  X
   8     8  X
   9     9     X
  10    10  X     X
  11    15     X  X
  12    14  X        X

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

Cf. A055932, A083720, A175343, A375281, A375615.

PARI
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A306869 Lexicographically earliest sequence of distinct positive terms such that the binary representation of the bitwise-OR of two consecutive terms has exactly one run of consecutive ones.

Original entry on oeis.org

1, 2, 3, 4, 6, 5, 7, 8, 12, 10, 13, 11, 14, 9, 15, 16, 24, 20, 26, 21, 27, 22, 25, 23, 28, 18, 29, 19, 30, 17, 31, 32, 48, 40, 52, 42, 53, 43, 54, 41, 55, 44, 50, 45, 51, 46, 49, 47, 56, 36, 58, 37, 59, 38, 57, 39, 60, 34, 61, 35, 62, 33, 63, 64, 96, 80, 104

Offset: 1

Rémy Sigrist, Mar 14 2019

This sequence has similarities with A175343; in both sequences, the binary representation of the bitwise OR of two consecutive terms has exactly one run of consecutive ones.

			The first terms, alongside the binary representation of a(n) OR a(n+1), are:
  a   a(n)  bin(a(n) OR a(n+1))
  --  ----  -------------------
   1     1                 11
   2     2                 11
   3     3                111
   4     4                110
   5     6                111
   6     5                111
   7     7               1111
   8     8               1100
   9    12               1110
  10    10               1111
  11    13               1111
  12    11               1111
  13    14               1111
  14     9               1111
  15    15              11111
  16    16              11000

Rémy Sigrist, Table of n, a(n) for n = 1..8192
Rémy Sigrist, PARI program for A306869

Cf. A069010, A175343.

PARI
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See Links section.
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A069010(a(n) OR a(n+1)) = 1.

cp's OEIS Frontend

A375579 Lexicographically earliest sequence of distinct positive integers such that the products of two consecutive terms belong to A055932.

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