|
|
A133321
|
|
Inserting any (identical) digit between adjacent digits of an odd semiprime k never yields a prime.
|
|
1
|
|
|
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
(list;
graph;
refs;
listen;
history;
text;
internal format)
|
|
|
OFFSET
|
1,1
|
|
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.
|
|
LINKS
|
|
|
EXAMPLE
|
121 is in the sequence because 10201, 11211, 12221, 13231, 14241, 15251, 16261, 17271, 18281, 19291 are all composite.
|
|
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 *)
|
|
CROSSREFS
|
|
|
KEYWORD
|
base,easy,nonn
|
|
AUTHOR
|
|
|
EXTENSIONS
|
|
|
STATUS
|
approved
|
|
|
|