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A366391 Numbers k such that A163511(k) is an eleventh power.

%I A366391 #15 Sep 21 2024 08:40:51
%S A366391 0,1024,2049,4099,8199,16399,32799,65599,131199,262399,524799,1049599,
%T A366391 2097152,2099199,4194305,4196352,4198399,8388611,8392705,8394752,
%U A366391 8396799,16777223,16785411,16789505,16791552,16793599,33554447,33570823,33579011,33583105,33585152,33587199,67108895,67141647,67158023,67166211,67170305
%N A366391 Numbers k such that A163511(k) is an eleventh power.
%C A366391 Equivalently, numbers k for which A332214(k), and also A332817(k) are eleventh powers.
%C A366391 The sequence is defined inductively as:
%C A366391  (a) it contains 0 and 1024,
%C A366391    and
%C A366391  (b) for any nonzero term a(n), (2*a(n)) + 1 and 2048*a(n) are also included as terms.
%C A366391 When iterating n -> 2n+1 mod 2047, starting from 1024 we get 1024, 2, 5, 11, 23, 47, 95, 191, 383, 767, 1535,  and then cycle starts again from 1024 (see A153893), while on the other hand, x^11 mod 2047 obtains values: 0, 1, 230, 322, 344, 368, 390, 482, 622, 712, 713, 942, 967, 1013, 1034, 1080, 1105, 1334, 1335, 1425, 1565, 1657, 1679, 1703, 1725, 1817, 2046. These sets have no terms in common, therefore there are no eleventh powers in this sequence after the initial 0.
%o A366391 (PARI)
%o A366391 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 A366391 isA366391v(n) = ispower(A163511(n),11);
%o A366391 (PARI) isA366391(n) = if(n<=1024, !(n%1024), if(n%2, isA366391((n-1)/2), if(n%2048, 0, isA366391(n>>11))));
%Y A366391 Positions of multiples of 11 in A365805.
%Y A366391 Sequence A243071(n^11), n >= 1, sorted into ascending order.
%Y A366391 Cf. A008455, A153893, A163511, A332214, A332817.
%Y A366391 Cf. also A365801, A365802, A365808, A366287.
%K A366391 nonn
%O A366391 1,2
%A A366391 _Antti Karttunen_, Oct 09 2023