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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.
This sequence contains no even numbers (A014076). - Robert G. Wilson v, Sep 22 2008
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
Cf. A143792.
Sequence in context: A154384 A327756 A210251 * A091113 A188159 A272600
KEYWORD
base,nonn
AUTHOR
Leroy Quet, Sep 01 2008
EXTENSIONS
a(7) and further terms from Robert G. Wilson v, Sep 22 2008
STATUS
approved

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Last modified March 28 04:13 EDT 2024. Contains 371235 sequences. (Running on oeis4.)