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

0, 1024, 2049, 4099, 8199, 16399, 32799, 65599, 131199, 262399, 524799, 1049599, 2097152, 2099199, 4194305, 4196352, 4198399, 8388611, 8392705, 8394752, 8396799, 16777223, 16785411, 16789505, 16791552, 16793599, 33554447, 33570823, 33579011, 33583105, 33585152, 33587199, 67108895, 67141647, 67158023, 67166211, 67170305

Offset

1,2

Comments

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

The sequence is defined inductively as:

(a) it contains 0 and 1024,

and

(b) for any nonzero term a(n), (2*a(n)) + 1 and 2048*a(n) are also included as terms.

When iterating n -> 2n+1 mod 2047, starting from 64 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.

Links

Table of n, a(n) for n=1..37.

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));
isA366391v(n) = ispower(A163511(n), 11);
(PARI) isA366391(n) = if(n<=1024, !(n%1024), if(n%2, isA366391((n-1)/2), if(n%2048, 0, isA366391(n>>11))));

Crossrefs

Positions of multiples of 11 in A365805.

Sequence A243071(n^11), n >= 1, sorted into ascending order.

Cf. A008455, A153893, A163511, A332214, A332817.

Cf. also A365801, A365802, A365808, A366287.

Sequence in context: A221260 A223065 A298607 * A195093 A258734 A195234

Adjacent sequences: A366388 A366389 A366390 * A366392 A366393 A366394

Keyword

nonn

Author

Antti Karttunen, Oct 09 2023

Status

approved