A365808 - OEIS

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A365808

Numbers k such that A163511(k) is a square.

0, 2, 5, 8, 11, 17, 20, 23, 32, 35, 41, 44, 47, 65, 68, 71, 80, 83, 89, 92, 95, 128, 131, 137, 140, 143, 161, 164, 167, 176, 179, 185, 188, 191, 257, 260, 263, 272, 275, 281, 284, 287, 320, 323, 329, 332, 335, 353, 356, 359, 368, 371, 377, 380, 383, 512, 515, 521, 524, 527, 545, 548, 551, 560, 563, 569, 572, 575

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OFFSET

1,2

COMMENTS

The sequence is defined inductively as:

(a) it contains 0 and 2,

and

(b) for any nonzero term a(n), (2*a(n)) + 1 and 4*a(n) are also included as terms.

Because the inductive definition guarantees that all terms after 0 are of the form 3k+2 (A016789), and because for any n >= 0, n^2 == 0 or 1 (mod 3), (i.e., squares are in A032766), it follows that there are no squares in this sequence after the initial 0.

LINKS

Table of n, a(n) for n=1..68.

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));

isA365808v2(n) = issquare(A163511(n));

(PARI) isA365808(n) = if(n<=2, !(n%2), if(n%2, isA365808((n-1)/2), if(n%4, 0, isA365808(n/4))));

CROSSREFS

Cf. A000290, A010052, A032766, A163511, A365807 (characteristic function).

Positions of even terms in A365805.

Sequence A243071(n^2), n >= 1, sorted into ascending order.