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 A109853 a(n) = A109852(2^n). 2
 1, 2, 5, 9, 13, 19, 29, 37, 43, 53, 61, 71, 79, 89, 101, 107, 113, 131, 139, 151, 163, 173, 181, 193, 199, 223, 229, 239, 251, 263, 271, 281, 293, 311, 317, 337, 349, 359, 373, 383, 397, 409, 421, 433, 443, 457, 463, 479, 491, 503, 521, 541, 557, 569, 577, 593 (list; graph; refs; listen; history; text; internal format)
 OFFSET 0,2 COMMENTS Conjecture: a(n) is prime if n is not 0 nor 2. Conjecture: a(n) is the (2n-2)nd prime for n>1. A109852(2^n-1): 1,3,5,11,17,23,31,41,47,59,67,73. - Robert G. Wilson v, Jun 14 2006 Conjecture: the Union of A109852(2^n-1) & A109852(2^n) is A046022: {1,2,3,4,5,7,11,13,17,19,23,29,31,37,41,43,47,53,59,61,67,71,73,79, ...,} and except for 4, equals A008578: The noncomposite numbers. - Robert G. Wilson v, Jun 14 2006 LINKS Rémy Sigrist, Table of n, a(n) for n = 0..1000 Rémy Sigrist, PARI program for A109853 MATHEMATICA f[s_] := Block[{k = 2, len = Length@s}, exp = Ceiling[Log[2, len]]; m = s[[2^exp - len + 1]]; While[MemberQ[s, k*m], k++ ]; Append[s, k*m]]; Rest@Nest[f, {1, 1}, 70]; t = Rest@Nest[f, {1, 1}, 2^14 + 3]; Table[t[[2^n]], {n, 0, 14}] (* Robert G. Wilson v, Jun 14 2006 *) PROG (PARI) See Links section. CROSSREFS Cf. A008578, A031215, A046022, A109852. Sequence in context: A120615 A038707 A290140 * A071705 A281171 A190713 Adjacent sequences:  A109850 A109851 A109852 * A109854 A109855 A109856 KEYWORD nonn AUTHOR Amarnath Murthy, Jul 07 2005 EXTENSIONS More terms from Robert G. Wilson v, Jun 14 2006 More terms from Rémy Sigrist, May 19 2019 STATUS approved

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Last modified December 1 16:44 EST 2021. Contains 349430 sequences. (Running on oeis4.)