cp's OEIS Frontend

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

%I A375029 #3 Jul 28 2024 12:54:06
%S A375029 1,2,4,5,10,12,15,20,22,33,36,38,57,60,70,77,88,90,105,112,114,171,
%T A375029 172,258,261,290,300,303,404,406,609,612,646,665,700,702,741,760,770,
%U A375029 847,848,954,957,1276,1278,1491,1498,1712,1713,3426,3428,4285,4290,5148
%N A375029 Lexicographically least increasing sequence such that for any prime number p, any run of consecutive multiples of p has length exactly 2.
%C A375029 This sequence is a variant of A280864.
%e A375029 The first terms, alongside their prime factors, are:
%e A375029   n   a(n)  Prime factors
%e A375029   --  ----  --------------------
%e A375029    1     1
%e A375029    2     2   2
%e A375029    3     4   2
%e A375029    4     5       5
%e A375029    5    10   2   5
%e A375029    6    12   2 3
%e A375029    7    15     3 5
%e A375029    8    20   2   5
%e A375029    9    22   2       11
%e A375029   10    33     3     11
%e A375029   11    36   2 3
%e A375029   12    38   2                19
%e A375029   13    57     3              19
%e A375029   14    60   2 3 5
%e A375029   15    70   2   5 7
%e A375029   16    77         7 11
%e A375029   17    88   2       11
%o A375029 (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 A375029 Cf. A280864.
%K A375029 nonn
%O A375029 1,2
%A A375029 _Rémy Sigrist_, Jul 28 2024