A365801 Numbers k such that A163511(k) is a cube.

0, 4, 9, 19, 32, 39, 65, 72, 79, 131, 145, 152, 159, 256, 263, 291, 305, 312, 319, 513, 520, 527, 576, 583, 611, 625, 632, 639, 1027, 1041, 1048, 1055, 1153, 1160, 1167, 1216, 1223, 1251, 1265, 1272, 1279, 2048, 2055, 2083, 2097, 2104, 2111, 2307, 2321, 2328, 2335, 2433, 2440, 2447, 2496, 2503, 2531, 2545, 2552

Offset: 1

Author

Antti Karttunen, Oct 01 2023

Keywords

• nonn

Comments

The sequence is defined inductively as:

(a) it contains 0 and 4,

and

(b) for any nonzero term a(n), (2*a(n)) + 1 and 8*a(n) are also included as terms.

Because the inductive definition guarantees that all terms after 0 are of the form 7k+2, 7k+4 or 7k+5 (A047378), and because for any n >= 0, n^3 == 0, 1 or 6 (mod 7), (i.e., cubes are in A047275), it follows that there are no cubes in this sequence after the initial 0.

Crossrefs

Positions of multiples of 3 in A365805.

Sequence A243071(n^3), n >= 1, sorted into ascending order.

Subsequence of A047378 (after the initial 0).

Subsequences: A013731, A153894.

Cf. A000578, A047275, A163511.

Cf. also A365802, A365808.

Programs

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));
isA365801(n) = ispower(A163511(n),3);

PARI

isA365801(n) = if(n<=4, !(n%4), if(n%2, isA365801((n-1)/2), if(n%8, 0, isA365801(n/8))));