A073251 - OEIS

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

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OFFSET

1,1

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

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 *)

PROG

(PARI) isok1(k) = !isprime(k) && issquarefree(k); \\ A000469

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

CROSSREFS

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

Sequence in context: A044552 A045939 A056809 * A005238 A052214 A063838

Adjacent sequences: A073248 A073249 A073250 * A073252 A073253 A073254

KEYWORD

nonn

AUTHOR

Reinhard Zumkeller, Jul 22 2002

EXTENSIONS

Edited by Klaus Brockhaus, Aug 07 2006

STATUS

approved