A133321 Inserting any (identical) digit between adjacent digits of an odd semiprime k never yields a prime.

15, 25, 35, 55, 65, 85, 95, 115, 121, 143, 145, 155, 185, 187, 205, 215, 235, 253, 265, 295, 299, 305, 335, 341, 355, 365, 393, 395, 411, 415, 437, 445, 451, 473, 485, 505, 515, 535, 545, 565, 583, 635, 655, 671, 679, 685, 695, 717, 745, 755, 781, 785, 815

Offset: 1

Author

Jonathan Vos Post, Oct 18 2007

Keywords

• base
• easy
• nonn

Comments

Odd semiprime analog of A050805. Trivially true for any digit if we substitute "even semiprime" for "odd semiprime." Trivially true for any semiprime which is a multiple of 5 (A001750). The nonmultiples of 5 in this sequence begin 121, 143, 187, 253, 299, 341.

Examples

			121 is in the sequence because 10201, 11211, 12221, 13231, 14241, 15251, 16261, 17271, 18281, 19291 are all composite.
		

Links

• Harvey P. Dale, Table of n, a(n) for n = 1..1000

Crossrefs

Cf. A001358, A001750, A050674-A050719, A050805, A050806.

Programs

Mathematica

Select[Select[Range[11,900,2],PrimeOmega[#]==2&],AllTrue[Table[ FromDigits[ Riffle[ IntegerDigits[#],n]],{n,0,9}],CompositeQ]&] (* Requires Mathematica version 10 or later *) (* Harvey P. Dale, Mar 07 2018 *)

Extensions

More terms from R. J. Mathar, Oct 22 2007