A062837 Numbers k such that k, 2*k+1, 3*k+1 are all squarefree.

2, 3, 6, 7, 10, 11, 14, 15, 19, 23, 26, 30, 34, 35, 38, 39, 42, 43, 46, 47, 51, 55, 59, 66, 70, 71, 74, 78, 79, 82, 86, 91, 95, 102, 106, 107, 110, 111, 115, 118, 119, 123, 127, 131, 134, 138, 142, 143, 146, 151, 154, 155, 159, 167, 170, 174, 178, 179, 182, 186

Offset

1,1

Comments

The asymptotic density of this sequence is (7/3) * Product_{p prime} (1 - 3/p^2) = (7/3) * A206256 = 0.292802955446... (Tsang, 1985). - Amiram Eldar, Feb 26 2024

Links

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

Kai-Man Tsang, The distribution of r-tuples of square-free numbers, Mathematika, Vol. 32, No. 2 (1985), pp. 265-275.

Mathematica

Select[Range[200], AllTrue[{#, 2#+1, 3#+1}, SquareFreeQ]&] (* Harvey P. Dale, Oct 20 2014 *)

Prog

(PARI) j=[]; for(n=1, 200, if(issquarefree(n) && issquarefree(2*n+1) && issquarefree(3*n+1), j=concat(j, n))); j

Crossrefs

Subsequence of A005117 and A117204.

Cf. A206256.

Sequence in context: A042964 A338064 A230375 * A190670 A226115 A359503

Adjacent sequences: A062834 A062835 A062836 * A062838 A062839 A062840

Keyword

nonn

Author

Jason Earls, Jul 21 2001

Status

approved