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A225728 Primes p such that sum of primorials (A143293) not including p as a factor is divisible by p. 0
3, 17, 967 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,1

COMMENTS

As in A002110, primorial(0)=1, and primorial(n) = primorial(n-1)*prime(n).

The next term, if it exists, is bigger than 10^8.

LINKS

Table of n, a(n) for n=1..3.

EXAMPLE

Sum of primorials not including 3 as a factor is 1 + 2 = 3. Because it's divisible by 3, the latter is in the sequence.

Sum of primorials not including 17 as a factor is 1 + 2 + 6 + 6*5 + 30*7 + 210*11 + 2310*13 = 32589. Because 32589 is divisible by 17, the latter is in the sequence.

PROG

(Python)

primes = [2]*2

primes[1] = 3

def addPrime(k):

  for p in primes:

    if k%p==0:  return

    if p*p > k:  break

  primes.append(k)

for n in range(5, 100000000, 6):

  addPrime(n)

  addPrime(n+2)

sum = 0

primorial = 1

for p in primes:

  sum += primorial

  primorial *= p

  if sum % p == 0:  print p,

(PARI) s=P=1; forprime(p=2, 1e6, s+=P*=p; if(s%p==0, print1(p", "))) \\ Charles R Greathouse IV, Mar 19 2014

(PARI) is(p)=if(!isprime(p), return(0)); my(s=Mod(1, p), P=s); forprime(q=2, p-1, s+=P*=q); s==0 \\ Charles R Greathouse IV, Mar 19 2014

CROSSREFS

Cf. A002110, A143293, A225727.

Sequence in context: A270816 A217957 A252730 * A175984 A051710 A215913

Adjacent sequences:  A225725 A225726 A225727 * A225729 A225730 A225731

KEYWORD

nonn,bref,hard,more

AUTHOR

Alex Ratushnyak, May 14 2013

STATUS

approved

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Last modified April 6 20:39 EDT 2020. Contains 333286 sequences. (Running on oeis4.)