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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 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.)