A333555 -id:A333555 - cp's OEIS frontend

A333556 a(n) = A333555(1) XOR ... XOR A333555(n) (where XOR denotes the bitwise XOR operator).

1, 3, 7, 15, 10, 26, 58, 43, 107, 121, 92, 220, 207, 232, 160, 134, 152, 408, 396, 430, 492, 262, 774, 784, 825, 862, 1008, 754, 718, 546, 1570, 1589, 1650, 1600, 1867, 1875, 2042, 1524, 1419, 1174, 3222, 3210, 3237, 3102, 3163, 3361, 3882, 3642, 2589, 2930

Offset: 1

Rémy Sigrist, Mar 26 2020

All terms are distinct.

			a(3) = A333555(1) XOR A333555(2) XOR A333555(3) = 1 XOR 2 XOR 4 = 7.

Rémy Sigrist, Table of n, a(n) for n = 1..8747
Rémy Sigrist, C program for A333556

Cf. A333555.

C
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See Links section.
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A333559 Lexicographically earliest infinite sequence of positive terms such that for any two distinct nonempty intervals, say [t, u] and [v, w], a(t) * ... * a(u) <> a(v) * ... * a(w).

Original entry on oeis.org

2, 3, 4, 5, 7, 8, 9, 10, 11, 13, 14, 15, 17, 16, 18, 19, 21, 22, 23, 25, 26, 27, 28, 29, 30, 31, 32, 33, 34, 36, 37, 38, 39, 40, 41, 42, 43, 44, 45, 46, 47, 48, 49, 50, 51, 52, 53, 54, 55, 57, 58, 59, 61, 62, 63, 64, 65, 66, 67, 68, 69, 70, 71, 73, 74, 75, 76

Offset: 1

Rémy Sigrist, Mar 26 2020

nonn

By necessity, all terms are distinct and strictly greater than 1.
This sequence is a variant of A101274.
Does every positive integer correspond to a product of consecutive terms?

			The values of a(i) * ... * a(j) for i <= j <= 7 are:
  i\j|  1  2   3    4    5     6      7
  ---+---------------------------------
    1|  2  6  24  120  840  6720  60480
    2|  .  3  12   60  420  3360  30240
    3|  .  .   4   20  140  1120  10080
    4|  .  .   .    5   35   280   2520
    5|  .  .   .    .    7    56    504
    6|  .  .   .    .    .     8     72
    7|  .  .   .    .    .     .      9

Rémy Sigrist, PARI program for A333559

Cf. A079854, A101274 (additive variant), A333555 (XOR variant).

PARI
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See Links section.
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a(n) = A079854(n+2) / A079854(n+1).

cp's OEIS Frontend

A333556 a(n) = A333555(1) XOR ... XOR A333555(n) (where XOR denotes the bitwise XOR operator).

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