A095678 Minimal sequence such that all triples of consecutive numbers have no common divisor greater than 1, but all three pairs within the triples are not coprime.

6, 10, 15, 12, 20, 45, 18, 40, 75, 24, 50, 135, 36, 80, 225, 48, 100, 375, 54, 160, 405, 72, 200, 675, 96, 250, 1125, 108, 320, 1215, 144, 400, 1875, 162, 500, 2025, 192, 640, 3375, 216, 800, 3645, 288, 1000, 5625, 324, 1250, 6075, 384, 1280, 9375, 432

Offset

1,1

Links

Amiram Eldar, Table of n, a(n) for n = 1..10000

Formula

gcd(a(n),a(n+1),a(n+2)) = 1, gcd(a(n),a(n+1)) > 1, gcd(a(n),a(n+2)) > 1 and gcd(a(n+1),a(n+2)) > 1.

A001221(a(n)) = 2; 2 <= A020639(a(n)) <= 3 <= A006530(a(n)) <= 5.

From Jianing Song, Jun 08 2022: (Start)

a(3n-2) = A033845(n) = 6*A003586(n);

a(3n-1) = A033846(n) = 10*A003592(n);

a(3n) = A033849(n) = 15*A003593(n). (End)

Sum_{n>=1} 1/a(n) = 7/8. - Amiram Eldar, Sep 29 2024

Mathematica

seq1[p_, q_, lim_] := Sort[Flatten[Table[p^i * q^j, {i, 1, Log[p, lim]}, {j, 1, Log[q, lim/p^i]}]]];
seq[lim_] := Module[{s1 = seq1[2, 3, lim], s2 = seq1[2, 5, lim], s3 = seq1[3, 5, lim], ns}, ns = Length[s3]; Flatten[Transpose[{s1[[1;; ns]], s2[[1;; ns]], s3}]]]; seq[10^4] (* Amiram Eldar, Sep 29 2024 *)

Crossrefs

Cf. A001221, A003586, A003592, A003593, A006530, A020639, A033845, A033846, A033849.

Sequence in context: A381741 A362600 A361606 * A339116 A151972 A094564

Adjacent sequences: A095675 A095676 A095677 * A095679 A095680 A095681

Keyword

nonn

Author

Reinhard Zumkeller, Jul 04 2004

Status

approved