

A064896


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


16



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.
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



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



KEYWORD

base,easy,nonn


AUTHOR



STATUS

approved



