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.

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

Offset

1,2

Comments

This sequence contains no primes.

This sequence contains no even numbers (A014076). - Robert G. Wilson v, Sep 22 2008

Links

Amiram Eldar, Table of n, a(n) for n = 1..10000

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 *)
npdQ[k_]:=Max[SequenceCount[IntegerDigits[k, 2], IntegerDigits[#, 2]]&/@FactorInteger[k][[;; , 1]]]==0; Join[{1}, Select[Range[600], npdQ]] (* Harvey P. Dale, Dec 03 2024 *)

Crossrefs

Cf. A143792.

Sequence in context: A154384 A327756 A210251 * A091113 A188159 A272600

Adjacent sequences: A143788 A143789 A143790 * A143792 A143793 A143794

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