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A143791
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A positive integer n is included if no prime divisor p of n, when p is represented in binary, occurs within n represented in binary.
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2
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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; internal format)
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OFFSET
| 1,2
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COMMENTS
| This sequence contains no primes.
This sequence contains no primes or even numbers (A014076). [From Robert G. Wilson v (rgwv(AT)rgwv.com), Sep 22 2008]
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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.
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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 &] [From Robert G. Wilson v (rgwv(AT)rgwv.com), Sep 22 2008]
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CROSSREFS
| Cf. A143792.
Sequence in context: A138786 A139392 A154384 * A091113 A188159 A108181
Adjacent sequences: A143788 A143789 A143790 * A143792 A143793 A143794
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KEYWORD
| base,nonn
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AUTHOR
| Leroy Quet Sep 01 2008
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EXTENSIONS
| a(7) and further terms from Robert G. Wilson v (rgwv(AT)rgwv.com), Sep 22 2008
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