A240593 The smaller of a pair of consecutive composite squarefree numbers (A120944) without any prime number between them.

14, 21, 33, 34, 38, 55, 57, 62, 65, 69, 74, 77, 85, 86, 91, 93, 94, 105, 110, 114, 115, 118, 119, 122, 129, 133, 141, 142, 143, 145, 154, 158, 159, 165, 174, 177, 182, 183, 185, 186, 187, 194, 201, 202, 203, 205, 206, 209, 213, 214, 215, 217, 218, 219, 221, 230, 235, 237, 246, 247, 253, 254, 258, 259, 265, 266, 273, 285, 286, 287, 290, 295, 298, 299

Offset

1,1

Comments

Supersequence of A121495.

Links

Table of n, a(n) for n=1..74.

Example

62 is in the sequence because A120944(20)=62, A120944(21)=65, without primes between them.

Mathematica

Select[Partition[Select[Range[400], CompositeQ[#]&&SquareFreeQ[#]&], 2, 1], PrimePi[ #[[1]]]==PrimePi[#[[2]]]&][[All, 1]] (* Harvey P. Dale, Apr 12 2020 *)

Prog

(PARI)
freesqrcomp(n)=issquarefree(n)&&!isprime(n)
nextfqc(n)={local(k); k=n+1; while(!freesqrcomp(k), k+=1); return(k)}
{for(i=2, 1000, if(freesqrcomp(i) && (nextfqc(i)<nextprime(i)), print1(i, ", ")))}

Crossrefs

Cf. A120944, A240592.

Sequence in context: A006625 A114382 A120141 * A121495 A263990 A253810

Adjacent sequences: A240590 A240591 A240592 * A240594 A240595 A240596

Keyword

nonn

Author

Antonio Roldán, Apr 08 2014

Status

approved