A366287 Numbers k such that A163511(k) is a seventh power.

0, 64, 129, 259, 519, 1039, 2079, 4159, 8192, 8319, 16385, 16512, 16639, 32771, 33025, 33152, 33279, 65543, 66051, 66305, 66432, 66559, 131087, 132103, 132611, 132865, 132992, 133119, 262175, 264207, 265223, 265731, 265985, 266112, 266239, 524351, 528415, 530447, 531463, 531971, 532225, 532352, 532479, 1048576, 1048703

Offset

1,2

Comments

Equivalently, numbers k for which A332214(k), and also A332817(k) are seventh powers.

The sequence is defined inductively as:

(a) it contains 0 and 64,

and

(b) for any nonzero term a(n), (2*a(n)) + 1 and 128*a(n) are also included as terms.

When iterating n -> 2n+1 mod 127, starting from 64 we get 64, 2, 5, 11, 23, 47, 95, and then cycle starts again from 64 (see A153893), while on the other hand, x^7 mod 127 obtains values: 0, 1, 19, 20, 22, 24, 28, 37, 52, 59, 68, 75, 90, 99, 103, 105, 107, 108, 126. These sets have no terms in common, therefore there are no seventh powers in this sequence after the initial 0.

Links

Table of n, a(n) for n=1..45.

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));
isA366287(n) = ispower(A163511(n), 7);
(PARI) isA366287(n) = if(n<=64, !(n%64), if(n%2, isA366287((n-1)/2), if(n%128, 0, isA366287(n>>7))));

Crossrefs

Positions of multiples of 7 in A365805.

Sequence A243071(n^7), n >= 1, sorted into ascending order.

Cf. A001015, A153893, A163511, A332214, A332817.

Cf. A365801, A365802, A365808, A366391.

Sequence in context: A031464 A045076 A235058 * A252088 A211254 A252081

Adjacent sequences: A366284 A366285 A366286 * A366288 A366289 A366290

Keyword

nonn

Author

Antti Karttunen, Oct 09 2023

Status

approved