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Lexicographically least increasing sequence such that for any prime number p, any run of consecutive multiples of p has length exactly 2.
3

%I #3 Jul 28 2024 12:54:06

%S 1,2,4,5,10,12,15,20,22,33,36,38,57,60,70,77,88,90,105,112,114,171,

%T 172,258,261,290,300,303,404,406,609,612,646,665,700,702,741,760,770,

%U 847,848,954,957,1276,1278,1491,1498,1712,1713,3426,3428,4285,4290,5148

%N Lexicographically least increasing sequence such that for any prime number p, any run of consecutive multiples of p has length exactly 2.

%C This sequence is a variant of A280864.

%e The first terms, alongside their prime factors, are:

%e n a(n) Prime factors

%e -- ---- --------------------

%e 1 1

%e 2 2 2

%e 3 4 2

%e 4 5 5

%e 5 10 2 5

%e 6 12 2 3

%e 7 15 3 5

%e 8 20 2 5

%e 9 22 2 11

%e 10 33 3 11

%e 11 36 2 3

%e 12 38 2 19

%e 13 57 3 19

%e 14 60 2 3 5

%e 15 70 2 5 7

%e 16 77 7 11

%e 17 88 2 11

%o (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;););); }

%Y Cf. A280864.

%K nonn

%O 1,2

%A _Rémy Sigrist_, Jul 28 2024