A382376 - OEIS

A382376

Lexicographically earliest sequence of distinct positive integers such that the number of distinct prime factors of adjacent terms differ exactly by one.

1, 2, 6, 3, 10, 4, 12, 5, 14, 7, 15, 8, 18, 9, 20, 11, 21, 13, 22, 16, 24, 17, 26, 19, 28, 23, 33, 25, 34, 27, 35, 29, 36, 30, 38, 31, 39, 32, 40, 37, 44, 41, 45, 42, 46, 43, 48, 47, 50, 49, 51, 53, 52, 59, 54, 60, 55, 61, 56, 64, 57, 66, 58, 67, 62, 70, 63

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OFFSET

1,2

COMMENTS

All primorial numbers appear in the sequence (we can use similar arguments as for A382357).

Conjecture: this sequence is a permutation of the positive integers.

LINKS

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

Rémy Sigrist, PARI program

EXAMPLE

The initial terms are:

n a(n) A001221(a(n))

-- ---- -------------

1 1 0

2 2 1

3 6 2

4 3 1

5 10 2

6 4 1

7 12 2

8 5 1

9 14 2

10 7 1

11 15 2

12 8 1

13 18 2

14 9 1

15 20 2

PROG

(PARI) \\ See Links section.

CROSSREFS

Cf. A001221, A382357, A382374, A382377.

Sequence in context: A276941 A143219 A109465 * A090705 A208547 A365810

Adjacent sequences: A382373 A382374 A382375 * A382377 A382378 A382379

KEYWORD

nonn

AUTHOR

Rémy Sigrist, Mar 23 2025

STATUS

approved