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%I #21 Aug 23 2018 02:13:25
%S 2,269,269,3823,8539,729551,1416329,23592593,1478674861,20458458289,
%T 7558026467353,201008815538749
%N Least prime p such that Sum_{q prime <= p} q is divisible by the first n primes.
%C a(1)-a(9) are taken from De Koninck's book.
%C The sequence of indices of these primes is 1, 57, 57, 531, 1065, 58751, 108243, 1483151, 73716417, 901526695, 264119914199, 6301058125383.
%D Jean-Marie De Koninck, Those Fascinating Numbers, Amer. Math. Soc., 2009, p. 66.
%e 2 + 3 + ... + 269 = 2 * 3 * 1145
%e 2 + 3 + ... + 269 = 2 * 3 * 5 * 229
%e 2 + 3 + ... + 3823 = 2 * 3 * 5 * 7 * 4473
%e 2 + 3 + ... + 8539 = 2 * 3 * ... * 11 * 1826
%e 2 + 3 + ... + 729551 = 2 * 3 * ... * 13 * 682263
%e 2 + 3 + ... + 1416329 = 2 * 3 * ... * 17 * 143884
%e 2 + 3 + ... + 23592593 = 2 * 3 * ... * 19 * 1742804
%e 2 + 3 + ... + 1478674861 = 2 * 3 * ... * 23 * 237859969
%e 2 + 3 + ... + 20458458289 = 2 * 3 * ... * 29 * 1392427664
%e 2 + 3 + ... + 7558026467353 = 2 * 3 * ... * 31 * 4886311486119
%e 2 + 3 + ... + 201008815538749 = 2 * 3 * ... * 37 * 83956482342243
%t c=0; pr=2; p=2; s=2; q=2; While[c<6, While[!Divisible[s, pr], q = NextPrime[q]; s+=q]; Print[ q]; c++; p = NextPrime[p]; pr*=p]
%o (PARI) my(c=0, pr=2, p=2, s=2, q=2); while(c<6, while(s%pr!=0, q = nextprime(q+1); s+=q); print1(q,", "); c++; p = nextprime(p+1); pr*=p)
%Y Cf. A051838.
%K nonn,more
%O 1,1
%A _Amiram Eldar_, Aug 20 2018
%E a(11) from _Giovanni Resta_, Aug 20 2018
%E a(12) from _Giovanni Resta_, Aug 22 2018
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