A318171 Least prime p such that Sum_{q prime <= p} q is divisible by the first n primes.

2, 269, 269, 3823, 8539, 729551, 1416329, 23592593, 1478674861, 20458458289, 7558026467353, 201008815538749

Offset: 1

Author

Amiram Eldar, Aug 20 2018

Keywords

• nonn
• more

Comments

a(1)-a(9) are taken from De Koninck's book.

The sequence of indices of these primes is 1, 57, 57, 531, 1065, 58751, 108243, 1483151, 73716417, 901526695, 264119914199, 6301058125383.

Examples

			2 + 3 + ... + 269 = 2 * 3 * 1145
2 + 3 + ... + 269 = 2 * 3 * 5 * 229
2 + 3 + ... + 3823 = 2 * 3 * 5 * 7 * 4473
2 + 3 + ... + 8539 = 2 * 3 * ... * 11 * 1826
2 + 3 + ... + 729551 = 2 * 3 * ... * 13 * 682263
2 + 3 + ... + 1416329 = 2 * 3 * ... * 17 * 143884
2 + 3 + ... + 23592593 = 2 * 3 * ... * 19 * 1742804
2 + 3 + ... + 1478674861 = 2 * 3 * ... * 23 * 237859969
2 + 3 + ... + 20458458289 = 2 * 3 * ... * 29 * 1392427664
2 + 3 + ... + 7558026467353 = 2 * 3 * ... * 31 * 4886311486119
2 + 3 + ... + 201008815538749 = 2 * 3 * ... * 37 * 83956482342243
		

References

• Jean-Marie De Koninck, Those Fascinating Numbers, Amer. Math. Soc., 2009, p. 66.

Crossrefs

Cf. A051838.

Programs

Mathematica

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]

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)

Extensions

a(11) from Giovanni Resta, Aug 20 2018

a(12) from Giovanni Resta, Aug 22 2018