A373782 Indices k such that A373390(k) and A373390(k+2) are not coprime.

2, 3, 4, 5, 6, 7, 8, 10, 11, 12, 14, 15, 16, 17, 18, 20, 21, 22, 23, 26, 27, 28, 29, 30, 31, 32, 33, 34, 37, 39, 40, 41, 43, 44, 45, 46, 47, 48, 49, 50, 52, 54, 55, 56, 57, 58, 59, 60, 63, 65, 66, 67, 68, 69, 70, 71, 72, 74, 76, 78, 80, 81, 82, 83, 84, 86, 88

Offset

1,1

Links

Michael De Vlieger, Table of n, a(n) for n = 1..10000

Michael De Vlieger, Plot a(n) at (x,y) = (a(n) mod 1000, -floor(a(n)/1000) - 1), n = 1..10^6 in white.

Example

Let s = A373390.
a(1) = 2 since s(2) | s(4), i.e., 2 | 4.
a(2) = 3 since s(3) | s(5), i.e., 3 | 9.
a(3) = 4 since s(4) | s(6), i.e., 4 | 8.
a(4) = 5 since s(5) | s(7), i.e., gcd(9, 15) = 3.
9 is not in the sequence since a(9) = 5 and a(11) = 7 are coprime.

Mathematica

c[_] := False; p[_] := False; nn = 90;
Array[Set[{a[#], c[#], p[#]}, {#, True, True}] &, 3]; i = a[2]; j = a[3]; u = 4;
Reap[Do[k = u;
  While[Or[c[k], ! CoprimeQ[j, k], NoneTrue[Set[s, #], p] &@
    FactorInteger[k][[All, 1]]], k++];
  Map[Set[p[#], True] &, s]; If[! CoprimeQ[i, k], Sow[n - 2]];
  Set[{a[n], c[k], i, j}, {k, True, j, k}];
  If[k == u, While[c[u], u++]], {n, 4, nn}] ][[-1, 1]]

Crossrefs

Cf. A373390, A373781.

Sequence in context: A339879 A274374 A007298 * A190856 A127033 A028826

Adjacent sequences: A373779 A373780 A373781 * A373783 A373784 A373785

Keyword

nonn,easy

Author

Michael De Vlieger, Jul 01 2024

Status

approved