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

5, 11, 17, 23, 35, 41, 47, 65, 71, 83, 89, 95, 131, 137, 143, 161, 167, 179, 185, 191, 257, 263, 275, 281, 287, 323, 329, 335, 353, 359, 371, 377, 383, 515, 521, 527, 545, 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

Offset

1,1

Comments

The sequence is defined inductively as follows:

(a) it contains all numbers of the form 2^(2e) + 1, e >= 1,

and

(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.

Contains no squares. See A365808 for a proof.

Links

Table of n, a(n) for n=1..63.

Index entries for sequences related to binary expansion of n

Prog

(PARI)
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));
isA365809(n) = (n%2 && issquare(A163511(n)));
(PARI)
A209229(n) = (n && !bitand(n, n-1));
isA365809(n) = if(n<=2, 0, my(v=valuation(n-1, 2)); if(A209229(n-1), !(v%2), (v%2)&&isA365809(n>>v)));

Crossrefs

Odd terms of A365808.

Cf. A016754, A052539 (subsequence without its initial 2), A163511.

Sequence in context: A252596 A096448 A351140 * A147305 A049755 A096449

Adjacent sequences: A365806 A365807 A365808 * A365810 A365811 A365812

Keyword

nonn

Author

Antti Karttunen, Oct 01 2023

Status

approved