cp's OEIS Frontend

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

%I A366287 #14 Oct 09 2023 15:50:13
%S A366287 0,64,129,259,519,1039,2079,4159,8192,8319,16385,16512,16639,32771,
%T A366287 33025,33152,33279,65543,66051,66305,66432,66559,131087,132103,132611,
%U A366287 132865,132992,133119,262175,264207,265223,265731,265985,266112,266239,524351,528415,530447,531463,531971,532225,532352,532479,1048576,1048703
%N A366287 Numbers k such that A163511(k) is a seventh power.
%C A366287 Equivalently, numbers k for which A332214(k), and also A332817(k) are seventh powers.
%C A366287 The sequence is defined inductively as:
%C A366287  (a) it contains 0 and 64,
%C A366287    and
%C A366287  (b) for any nonzero term a(n), (2*a(n)) + 1 and 128*a(n) are also included as terms.
%C A366287 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.
%o A366287 (PARI)
%o A366287 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));
%o A366287 isA366287(n) = ispower(A163511(n),7);
%o A366287 (PARI) isA366287(n) = if(n<=64, !(n%64), if(n%2, isA366287((n-1)/2), if(n%128, 0, isA366287(n>>7))));
%Y A366287 Positions of multiples of 7 in A365805.
%Y A366287 Sequence A243071(n^7), n >= 1, sorted into ascending order.
%Y A366287 Cf. A001015, A153893, A163511, A332214, A332817.
%Y A366287 Cf. A365801, A365802, A365808, A366391.
%K A366287 nonn
%O A366287 1,2
%A A366287 _Antti Karttunen_, Oct 09 2023