cp's OEIS Frontend

A365809 Odd numbers k such that A163511(k) is a square.

%I A365809 #12 Feb 12 2025 18:48:06
%S A365809 5,11,17,23,35,41,47,65,71,83,89,95,131,137,143,161,167,179,185,191,
%T A365809 257,263,275,281,287,323,329,335,353,359,371,377,383,515,521,527,545,
%U A365809 551,563,569,575,641,647,659,665,671,707,713,719,737,743,755,761,767,1025,1031,1043,1049,1055,1091,1097,1103,1121
%N A365809 Odd numbers k such that A163511(k) is a square.
%C A365809 The sequence is defined inductively as follows:
%C A365809  (a) it contains all numbers of the form 2^(2e) + 1, e >= 1,
%C A365809    and
%C A365809  (b) for any term a(n) and any e >= 0, (2^(2e+1) * a(n)) + 1 is also included as a term. There are no other kind of terms.
%C A365809 Contains no squares. See A365808 for a proof.
%H A365809 <a href="/index/Bi#binary">Index entries for sequences related to binary expansion of n</a>
%o A365809 (PARI)
%o A365809 A163511(n) = if(!n, 1, my(p=2, t=1); while(n>1, if(!(n%2), (t*=p), p=nextprime(1+p)); n >>= 1); (t*p));
%o A365809 isA365809(n) = (n%2 && issquare(A163511(n)));
%o A365809 (PARI)
%o A365809 A209229(n) = (n && !bitand(n,n-1));
%o A365809 isA365809(n) = if(n<=2,0,my(v=valuation(n-1,2)); if(A209229(n-1),!(v%2),(v%2)&&isA365809(n>>v)));
%o A365809 (Python)
%o A365809 from itertools import count, islice
%o A365809 def A365809_gen(): # generator of terms
%o A365809     return map(lambda n:(3*(n+1)>>1)-1,filter(lambda n:n&3==3 and not '00' in bin(n),count(1)))
%o A365809 A365809_list = list(islice(A365809_gen(),63)) # _Chai Wah Wu_, Feb 12 2025
%Y A365809 Odd terms of A365808.
%Y A365809 Cf. A016754, A052539 (subsequence without its initial 2), A163511.
%K A365809 nonn
%O A365809 1,1
%A A365809 _Antti Karttunen_, Oct 01 2023