A073251 Numbers k such that k, k+1 and k+2 are nonprime and squarefree.

33, 85, 93, 141, 185, 201, 213, 217, 253, 265, 285, 301, 321, 393, 445, 453, 469, 481, 517, 533, 553, 581, 589, 609, 633, 669, 697, 705, 713, 753, 777, 789, 793, 805, 813, 869, 893, 897, 901, 913, 921, 933, 957, 985, 993, 1001, 1005, 1041, 1045, 1065, 1113

Offset: 1

Author

Reinhard Zumkeller, Jul 22 2002

Keywords

• nonn

Comments

k-1 and k+3 are not squarefree. Proof: k is odd, otherwise k or k+2 would be divisible by 4. Thus k+1 is even and not divisible by 4, hence k-1 and k+3 are divisible by 4.

Links

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

Crossrefs

Cf. A000469, A005117, A007675, A073249, A073250, A121495.

Programs

Mathematica

f[upto_]:=Module[{pp=PrimePi[upto],n},lst=Partition[Complement[Range[upto], Prime[Range[pp]]],3,1];Transpose[Select[lst,And@@SquareFreeQ/@#&]][[1]]]; f[1200] (* Harvey P. Dale, Mar 21 2011 *)

PARI

isok1(k) = !isprime(k) && issquarefree(k); \\ A000469
isok(k) = isok1(k) && isok1(k+1) && isok1(k+2); \\ Michel Marcus, Mar 25 2021

Extensions

Edited by Klaus Brockhaus, Aug 07 2006