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Slowest-growing sequence of odd primes whose reciprocals sum to 1.
4

%I #22 Jun 27 2024 01:36:11

%S 3,5,7,11,13,17,19,23,967,101419,2000490719,106298338760698351,

%T 586903266015193517540253132922939,

%U 3494365451928289992209032562272585187947069047023572601254975717

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

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

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

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

%H Amiram Eldar, <a href="/A225669/b225669.txt">Table of n, a(n) for n = 1..18</a>

%e 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.

%t 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]

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

%K nonn

%O 1,1

%A _Jonathan Sondow_, May 11 2013