|
|
A143791
|
|
A positive integer k is included if no prime divisor p of k, when p is represented in binary, occurs within k represented in binary.
|
|
3
|
|
|
1, 9, 21, 25, 33, 35, 49, 65, 69, 77, 81, 115, 121, 129, 133, 143, 145, 161, 169, 203, 209, 217, 253, 259, 261, 265, 273, 275, 289, 295, 297, 299, 301, 305, 319, 321, 323, 329, 341, 361, 377, 385, 391, 403, 415, 427, 437, 451, 481, 505, 513, 515, 517, 527, 529
(list;
graph;
refs;
listen;
history;
text;
internal format)
|
|
|
OFFSET
|
1,2
|
|
COMMENTS
|
This sequence contains no primes.
|
|
LINKS
|
|
|
EXAMPLE
|
21 is binary is 10101. The prime divisors of 21 are 3 and 7. 3 is 11 in binary, which does not occur within 10101. 7 is 111 in binary, which also does not occur within 10101. So 21 is in the sequence.
On the other hand, 27 in binary is 11011. The only prime divisor of 27 is 3, which is 11 in binary. 11 does occur (twice) within 11011 like so: (11)0(11). So 27 is not in the sequence.
|
|
MATHEMATICA
|
f[n_] := Block[{nb = ToString@ FromDigits@ IntegerDigits[n, 2], psb = ToString@ FromDigits@ IntegerDigits[ #, 2] & /@ First@ Transpose@ FactorInteger@ n, c = 0, k = 1}, lmt = 1 + Length@ psb; While[ k < lmt, If[ StringCount[ nb, psb[[k]]] > 0, c++ ]; k++ ]; c]; f[1] = 0; Select[ Range@ 1000, f@# == 0 &] (* Robert G. Wilson v, Sep 22 2008 *)
|
|
CROSSREFS
|
|
|
KEYWORD
|
base,nonn
|
|
AUTHOR
|
|
|
EXTENSIONS
|
|
|
STATUS
|
approved
|
|
|
|