A226124 Denominators of signed reciprocal primes with sums converging to 1.

2, 3, 5, 29, 863, 107251, 1519341947, 1028110904472525023, 18408375793288791212165960272609427, 12833942597163525070720542528785599268668682079686196789779156965969

Offset

1,1

Comments

The algorithm at A226049, with r = 1 and f(n) = 1/prime(n), gives the sum 1/2 + 1/3 + 1/5 - 1/29 + 1/863 - 1/107251 + 1/1519341947 - ... = 1, of which the denominators on the left side comprise this sequence.

Links

Amiram Eldar, Table of n, a(n) for n = 1..14

Example

1/2 + 1/3 + 1/5 - 1/29 + 1/863 - 1/107251 + 1/1519341947 differs from 1 by less than 10^(-18).

Mathematica

p[n_] := Prime[n]; q[x_] := PrimePi[x]; r = 1; u = 1/2 + 1/3 + 1/5; c[1] = q[1/(u - r)]; c[2] = q[1/(r - u + 1/p[c[1]])]; c[3] = q[1/(u - r - 1/p[c[1]] + 1/p[c[2]])]; c[4] = q[1/(r - u + 1/p[c[1]] - 1/p[c[2]] + 1/p[c[3]])]; Union[{2, 3, 5}, Table[p[c[i]], {i, 1, 4}]]
seq={2, 3, 5}; sum=Total@(1/seq); While[Length[seq]<10, p=NextPrime[Abs[1/(sum-1)], -1]; sum+=Sign[1-sum]/p; AppendTo[seq, p]]; seq (* Amiram Eldar, Mar 13 2019 *)

Crossrefs

Cf. A226049.

Sequence in context: A107451 A093490 A073309 * A110389 A083388 A090475

Adjacent sequences: A226121 A226122 A226123 * A226125 A226126 A226127

Keyword

nonn

Author

Clark Kimberling, May 27 2013

Extensions

a(8)-a(10) from Amiram Eldar, Mar 13 2019

Status

approved