A127515 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 prime (or is 1).

1, 2, 3, 5, 4, 7, 8, 6, 9, 14, 10, 11, 12, 15, 17, 16, 18, 29, 22, 20, 23, 40, 13, 21, 19, 26, 28, 44, 27, 25, 31, 35, 24, 36, 32, 37, 38, 49, 48, 42, 41, 30, 33, 45, 61, 43, 56, 51, 64, 34, 72, 63, 66, 46, 55, 68, 50, 67, 52, 39, 53, 74, 93, 54, 87, 75, 59, 71, 62, 60, 73, 58

Offset

1,2

Comments

A127516(n)/A127517(n) is sum{k=1 to n} 1/a(k). This sequence, A127515, 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 +1/2 + 1/3 = 11/6. 11/6 + 1/4 = 25/12; but 25 is composite, so a(4) is not 4. But 11/6 +1/5 = 61/30. And since 61 is prime, then a(4) = 5.

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] || ! (n == 1 || PrimeQ[n]), k++ ]; Append[l, k]]; Nest[g, {}, 72] (* Ray Chandler, Jan 22 2007 *)

Crossrefs

Cf. A127516, A127517, A127518.

Cf. A076474, A134411.

Sequence in context: A276345 A257455 A328971 * A332565 A256996 A316668

Adjacent sequences: A127512 A127513 A127514 * A127516 A127517 A127518

Keyword

nonn

Author

Leroy Quet, Jan 17 2007

Extensions

Extended by Ray Chandler, Jan 22 2007

Status

approved