cp's OEIS Frontend

A383927 Binary echo numbers: positive integers k such that the gpf(k-1) is a suffix of k when gpf(k-1) and k are written in binary.

%I A383927 #17 May 23 2025 10:19:09
%S A383927 7,15,19,21,55,61,63,71,101,115,127,155,157,163,181,255,273,295,301,
%T A383927 331,349,351,365,487,501,541,573,585,599,631,687,711,723,741,781,817,
%U A383927 827,901,1055,1135,1211,1277,1331,1361,1387,1405,1459,1471,1475,1501,1621,1641,1751
%N A383927 Binary echo numbers: positive integers k such that the gpf(k-1) is a suffix of k when gpf(k-1) and k are written in binary.
%C A383927 No term may be even, since if k were even, then k-1 would be odd and have only odd prime factors, none of which could be a suffix of k.
%H A383927 Vincenzo Librandi, <a href="/A383927/b383927.txt">Table of n, a(n) for n = 1..3158</a>
%e A383927 7 is a term since 7 = 111_2, the gpf(6) = 3 = 11_2, and 11 is a suffix of 111.
%e A383927 21 is a term since 21 = 10101_2, the gpf(20) = 5 = 101_2, and 101 is a suffix of 10101.
%t A383927 Select[Range@2000,(f=IntegerDigits[FactorInteger[#-1][[-1,1]],2])==IntegerDigits[#,2][[-Length@f;;]]&] (* _Giorgos Kalogeropoulos_, May 15 2025 *)
%o A383927 (Python)
%o A383927 from sympy import factorint
%o A383927 def ok(n): return n > 2 and bin(n)[2:].endswith(bin(max(factorint(n-1)))[2:])
%o A383927 print([k for k in range(1800) if ok(k)]) # _Michael S. Branicky_, May 15 2025
%Y A383927 Binary analog of A383896 (and of A383296).
%Y A383927 Cf. A006530.
%K A383927 nonn,base
%O A383927 1,1
%A A383927 _Michael S. Branicky_, May 15 2025