A318171 - OEIS

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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

(list; graph; refs; listen; history; text; internal format)

OFFSET

1,1

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.

REFERENCES

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

LINKS

Table of n, a(n) for n=1..12.

EXAMPLE

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

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]

PROG

(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)

CROSSREFS

Cf. A051838.

Sequence in context: A238983 A188964 A278771 * A324596 A007512 A048534

Adjacent sequences: A318168 A318169 A318170 * A318172 A318173 A318174

KEYWORD

nonn,more

AUTHOR

Amiram Eldar, Aug 20 2018

EXTENSIONS

a(11) from Giovanni Resta, Aug 20 2018

a(12) from Giovanni Resta, Aug 22 2018

STATUS

approved