A375029 Lexicographically least increasing sequence such that for any prime number p, any run of consecutive multiples of p has length exactly 2.

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

Author

Rémy Sigrist, Jul 28 2024

Keywords

• nonn

Comments

This sequence is a variant of A280864.

Examples

			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
		

Crossrefs

Cf. A280864.

Programs

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;););); }