This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.
%I A143791 #17 Dec 03 2024 13:51:08
%S A143791 1,9,21,25,33,35,49,65,69,77,81,115,121,129,133,143,145,161,169,203,
%T A143791 209,217,253,259,261,265,273,275,289,295,297,299,301,305,319,321,323,
%U A143791 329,341,361,377,385,391,403,415,427,437,451,481,505,513,515,517,527,529
%N 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.
%C A143791 This sequence contains no primes.
%C A143791 This sequence contains no even numbers (A014076). - _Robert G. Wilson v_, Sep 22 2008
%H A143791 Amiram Eldar, <a href="/A143791/b143791.txt">Table of n, a(n) for n = 1..10000</a>
%e A143791 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.
%e A143791 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.
%t A143791 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 *)
%t A143791 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 *)
%Y A143791 Cf. A143792.
%K A143791 base,nonn
%O A143791 1,2
%A A143791 _Leroy Quet_, Sep 01 2008
%E A143791 a(7) and further terms from _Robert G. Wilson v_, Sep 22 2008