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).

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

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

Table of n, a(n) for n=1..72.

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

Cf. A127515, A127519, A127520.

Sequence in context: A038226 A095866 A067569 * A176118 A151693 A007284

Adjacent sequences: A127515 A127516 A127517 * A127519 A127520 A127521

Keyword

nonn

Author

Leroy Quet, Jan 17 2007

Extensions

Extended by Ray Chandler, Jan 22 2007

Status

approved