A254069 a(n) = smallest k such that none of 4*k - 4*j + 2 and 4*k + 4*j - 2, j = 0, 1, 2, .. n, are squarefree.

13, 13, 1263, 837140

Offset

0,1

Comments

a(4) > 10^8.

Links

Table of n, a(n) for n=0..3.

Example

a(0) = 13 because none of 4*13 - 4*0 + 2 = 54, 4*13 + 4*0 - 2 = 50 are squarefree,
a(1) = 13 because none of 4*13 - 4*1 + 2 = 50, 4*13 + 4*1 - 2 = 54 are squarefree,
a(2) = 1263 because none of 4*1263 - 4*2 + 2 = 5046, 4*1263 - 4*1 + 2 = 5050, 4*1263 + 4*1 - 2 = 5054, 4*1263 + 4*2 - 2 = 5058 are squarefree.

Mathematica

{1}~Join~Table[k = 0; While[! And[NoneTrue[4 k + 2 # & /@ Range@ n, SquareFreeQ], NoneTrue[4 k - 2 # & /@ Range@ n, SquareFreeQ]], k++]; k, {n, 6}] (* Michael De Vlieger, May 09 2015, Version 10 *)

Prog

(PARI) ok(n, k)=for(j=1, n, if(issquarefree(4*k-4*j+2) || issquarefree(4*k+4*j-2), return(0))); 1
a(n)=my(k); while(!ok(n, k++), ); k \\ Charles R Greathouse IV, May 22 2015

Crossrefs

Cf. A257115.

Sequence in context: A020553 A094461 A186070 * A309990 A196461 A371764

Adjacent sequences: A254066 A254067 A254068 * A254070 A254071 A254072

Keyword

nonn,more

Author

Juri-Stepan Gerasimov, May 03 2015

Status

approved