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A373782
Indices k such that A373390(k) and A373390(k+2) are not coprime.
2
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, 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
Sequence in context: A339879 A274374 A007298 * A190856 A127033 A028826
KEYWORD
nonn,easy
AUTHOR
Michael De Vlieger, Jul 01 2024
STATUS
approved