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

Author

Antti Karttunen, Oct 09 2023

Keywords

• nonn

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.

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.

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));
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))));