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A320441 Numbers whose binary expansion is quasiperiodic. 1
3, 7, 10, 15, 21, 31, 36, 42, 45, 54, 63, 73, 85, 91, 109, 127, 136, 146, 153, 170, 173, 181, 182, 187, 204, 219, 221, 238, 255, 273, 292, 307, 341, 365, 375, 409, 438, 443, 477, 511, 528, 546, 561, 585, 594, 614, 627, 660, 682, 685, 693, 725, 726, 731, 750 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,1

COMMENTS

The binary representation of a term (ignoring leading zeros) can be covered by (possibly overlapping) occurrences of one of its proper prefix.

This sequence contains A121016.

For any k > 0, there are A320434(k)/2 terms with binary length k.

LINKS

Table of n, a(n) for n=1..55.

Rémy Sigrist, Scatterplot of the first difference of the first 100000 terms

FORMULA

A020330(a(n)) belongs to the sequence for any n > 0.

A297405(a(n)) belongs to the sequence for any n > 0.

EXAMPLE

The first terms, alongside their binary representations and prefixes, are:

  n   a(n)  bin(a(n))  prefix

  --  ----  ---------  ------

   1     3         11       1

   2     7        111       1

   3    10       1010      10

   4    15       1111       1

   5    21      10101     101

   6    31      11111       1

   7    36     100100     100

   8    42     101010      10

   9    45     101101     101

  10    54     110110     110

  11    63     111111       1

  12    73    1001001    1001

PROG

(PARI) isok(w) = { my (tt=0); for (l=1, oo, my (t=w%(2^l)); if (t!=tt, if (t==w, return (0)); my (r=w, g=l); while (g-->=0 && r>=t, r \= 2; if (r%

(2^l)==t, if (r==t, return (1), g=l))); tt = t)) }

CROSSREFS

Cf. A020330, A121016, A297405, A320434.

Sequence in context: A292662 A294477 A085145 * A143101 A307612 A330160

Adjacent sequences:  A320438 A320439 A320440 * A320442 A320443 A320444

KEYWORD

nonn,base

AUTHOR

Rémy Sigrist, Jan 09 2019

STATUS

approved

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Last modified January 24 16:41 EST 2020. Contains 331208 sequences. (Running on oeis4.)