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A375029
Lexicographically least increasing sequence such that for any prime number p, any run of consecutive multiples of p has length exactly 2.
3
1, 2, 4, 5, 10, 12, 15, 20, 22, 33, 36, 38, 57, 60, 70, 77, 88, 90, 105, 112, 114, 171, 172, 258, 261, 290, 300, 303, 404, 406, 609, 612, 646, 665, 700, 702, 741, 760, 770, 847, 848, 954, 957, 1276, 1278, 1491, 1498, 1712, 1713, 3426, 3428, 4285, 4290, 5148
OFFSET
1,2
COMMENTS
This sequence is a variant of A280864.
EXAMPLE
The first terms, alongside their prime factors, are:
n a(n) Prime factors
-- ---- --------------------
1 1
2 2 2
3 4 2
4 5 5
5 10 2 5
6 12 2 3
7 15 3 5
8 20 2 5
9 22 2 11
10 33 3 11
11 36 2 3
12 38 2 19
13 57 3 19
14 60 2 3 5
15 70 2 5 7
16 77 7 11
17 88 2 11
PROG
(PARI) { p = 0; r = 1; m = 1; for (n = 1, 54, forstep (v = ceil((p+1)/m)*m, oo, m, if (gcd(v, r)==m, print1 (v", "); r = vecprod(factor(p = v)[, 1]~); m = r / m; break; ); ); ); }
CROSSREFS
Cf. A280864.
Sequence in context: A325095 A120491 A177186 * A260385 A355149 A022944
KEYWORD
nonn
AUTHOR
Rémy Sigrist, Jul 28 2024
STATUS
approved