

A064896


Numbers of the form (2^{mr}1)/(2^r1) for positive integers m, r.


14



1, 3, 5, 7, 9, 15, 17, 21, 31, 33, 63, 65, 73, 85, 127, 129, 255, 257, 273, 341, 511, 513, 585, 1023, 1025, 1057, 1365, 2047, 2049, 4095, 4097, 4161, 4369, 4681, 5461, 8191, 8193, 16383, 16385, 16513, 21845, 32767, 32769, 33825, 37449, 65535, 65537
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OFFSET

1,2


COMMENTS

Binary expansion of n consists of single 1's diluted by (possibly empty) equalsized blocks of 0's.
A064894(a(n)) = A056538(n)
According to Stolarsky's Theorem 2.1, all numbers in this sequence are sturdy numbers; this sequence is a subsequence of A125121.  T. D. Noe, Jul 21 2008


LINKS

T. D. Noe, Table of n, a(n) for n=1..1000
T. Chinburg and M. Henriksen, Sums of kth powers in the ring of polynomials with integer coefficients, Acta Arithmetica, 29 (1976), 227250.
K. B. Stolarsky, Integers whose multiples have anomalous digital frequencies, Acta Arithmetica, 38 (1980), 117128.


EXAMPLE

73 is included because it is 1001001 in binary, whose 1's are diluted by blocks of two 0's.


MAPLE

f := proc(p) local m, r, t1; t1 := {}; for m from 1 to 10 do for r from 1 to 10 do t1 := {op(t1), (p^(m*r)1)/(p^r1)}; od: od: sort(convert(t1, list)); end; f(2); # very crude!
# Alternative:
N:= 10^6: # to get all terms <= N
A:= sort(convert({1, seq(seq((2^(m*r)1)/(2^r1), m=2..1/r*ilog2(N*(2^r1)+1)), r=1..ilog2(N1))}, list)); # Robert Israel, Jun 12 2015


PROG

(PARI) lista(nn) = {v = [1]; x = (2^nn1); for (m=2, nn, r = 1; while ((y = (2^(m*r)1)/(2^r1)) <=x, v = Set(concat(v, y)); r++); ); v; } \\ Michel Marcus, Jun 12 2015


CROSSREFS

Cf. A064894, A056538.
Cf. A076270 (k=3), A076275 (k=4), A076284 (k=5), A076285 (k=6), A076286 (k=7), A076287 (k=8), A076288 (k=9), A076289 (k=10).
Primes in this sequence: A245730.
Sequence in context: A006995 A163410 A235264 * A076188 A265852 A073674
Adjacent sequences: A064893 A064894 A064895 * A064897 A064898 A064899


KEYWORD

base,easy,nonn


AUTHOR

Marc LeBrun, Oct 11 2001


STATUS

approved



