A255746 Squarefree semiprimes n such that n+4 is also a squarefree semiprime.

6, 10, 22, 34, 35, 51, 58, 65, 82, 87, 91, 111, 115, 118, 119, 129, 141, 142, 155, 183, 201, 202, 205, 209, 213, 214, 215, 217, 249, 274, 287, 291, 295, 298, 299, 301, 305, 319, 323, 335, 358, 377, 382, 391, 394, 403, 407, 411, 413, 447, 454, 469, 478, 481

Offset

1,1

Comments

Conjecturally, the sequence is infinite.

Links

Peter J. C. Moses, Table of n, a(n) for n = 1..1000

Formula

A000005(a(n)) = A000005(a(n)+4) = 4.

Example

65 = 5*13; 65 + 4 = 69 = 3*23. So 65 is in the sequence.

Mathematica

Select[Range@ 500, And[SquareFreeQ@ #, PrimeOmega@ # == 2, SquareFreeQ[# + 4], PrimeOmega[# + 4] == 2] &] (* Michael De Vlieger, Jul 12 2015 *)

Prog

(PARI) main(size)={ v=vector(size); i=0; m=1; while(i<size, if(omega(m)==2&&omega(m+4)==2&&issquarefree(m)&&issquarefree(m+4), v[i++]=m); m++; ); return(v); } /* Anders Hellström, Jul 11 2015 */

Crossrefs

Cf. A000005, A001358, A005117, A175648.

Sequence in context: A365064 A157037 A189992 * A082917 A001172 A339437

Adjacent sequences: A255743 A255744 A255745 * A255747 A255748 A255749

Keyword

nonn

Author

Vladimir Shevelev, Jul 11 2015

Extensions

More terms from Peter J. C. Moses, Jul 11 2015

Status

approved