A225669 Slowest-growing sequence of odd primes whose reciprocals sum to 1.

3, 5, 7, 11, 13, 17, 19, 23, 967, 101419, 2000490719, 106298338760698351, 586903266015193517540253132922939, 3494365451928289992209032562272585187947069047023572601254975717

Offset: 1

Author

Jonathan Sondow, May 11 2013

Keywords

• nonn

Comments

See comments, references, and links in A075442 = slowest-growing sequence of primes whose reciprocals sum to 1.

a(n) = 3, 5, 7, 11, 13, 17, 19, 23, 967, ..., so A225671(2) = 23.

Examples

			Since 1/3 + 1/5 + 1/7 + 1/11 + 1/13 + 1/17 + 1/19 + 1/23 < 1, the first eight odd primes are members. The ninth is not, because adding 1/29 pushes the sum over 1.
		

References

• Popular Computing (Calabasas, CA), Problem 175: A Sum of a Different Kind, Vol. 5 (No. 50, May 1977), p. PC50-8.

Links

• Amiram Eldar, Table of n, a(n) for n = 1..18

Crossrefs

Cf. A000058, A075442, A046689, A136616, A181503, A225670, A225671.

Programs

Mathematica

a[n_] := a[n] = Block[{sm = Sum[1/(a[i]), {i, n - 1}]}, NextPrime[ Max[ a[n - 1], 1/(1 - sm)]]]; a[0] = 2; Array[a, 14]