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

Author

Leroy Quet, Sep 01 2008

Keywords

• base
• nonn

Comments

This sequence contains no primes.

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

Examples

			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.
		

Links

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

Crossrefs

Cf. A143792.

Programs

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 *)

Extensions

a(7) and further terms from Robert G. Wilson v, Sep 22 2008