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A127518 a(n) is the smallest positive integer which does not occur earlier in the sequence and is such that sum{k=1 to n} 1/a(k) has a numerator which is composite (or is 1). 4
1, 3, 8, 10, 2, 7, 4, 5, 6, 9, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 22, 21, 23, 24, 25, 27, 26, 28, 29, 30, 31, 32, 33, 34, 35, 36, 37, 38, 39, 40, 43, 41, 42, 44, 45, 46, 47, 48, 49, 50, 51, 52, 53, 54, 55, 57, 56, 58, 59, 60, 61, 63, 62, 64, 65, 66, 67, 68, 71, 69, 70, 72 (list; graph; refs; listen; history; text; internal format)
OFFSET
1,2
COMMENTS
A127519(n)/A127520(n) is sum{k=1 to n} 1/a(k). This sequence, A127518, seems to be a permutation of the positive integers.
LINKS
EXAMPLE
1/a(1) + 1/a(2) +1/a(3) = 1 +1/3 + 1/8 = 35/24. 35/24 + 1/2 = 47/24; but 47 is prime, so a(4) is not 2. Likewise, an m of 4,5,6,7 and 9 give a numerator for (35/24 +1/m) which is prime. But 35/24 + 1/10 = 187/120. And since 187 = 11*17 is composite, then a(4) = 10.
MATHEMATICA
f[l_List] := Sum[1/l[[k]], {k, Length[l]}]; g[l_List] := Block[{k = 1, n}, While[n = Numerator[f[Append[l, k]]]; MemberQ[l, k] || PrimeQ[n], k++ ]; Append[l, k]]; Nest[g, {}, 75] (* Ray Chandler, Jan 22 2007 *)
CROSSREFS
Sequence in context: A038226 A095866 A067569 * A176118 A151693 A007284
KEYWORD
nonn
AUTHOR
Leroy Quet, Jan 17 2007
EXTENSIONS
Extended by Ray Chandler, Jan 22 2007
STATUS
approved

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Last modified March 28 11:59 EDT 2024. Contains 371254 sequences. (Running on oeis4.)