|
| |
|
|
A066735
|
|
Primes p dividing 1 + the product of the primes less than p.
|
|
2
| | |
|
|
|
OFFSET
| 1,1
|
|
|
COMMENTS
| Comment from Levai Gabor [L'{e}vai G'{a}bor], (gablevai(AT)vipmail.hu), Nov 23, 2004: "Let p(1)=2, p(2)=3, p(3)=5, ... denote the primes and let E(n) = 1 + p(1) * p(2) * ... * p(n). For k >= 1, list the primes p such that p(n+k) | E(n). For k=1 we get this sequence, for k=2 we get A100465.
"For k >= 3 the known results are as follows: if k = 3: no solutions for p < 80000000; if k = 4: 463, 2908123 and no others for p < 80000000; if k = 5: 61, 73 and no others for p < 80000000; if k = 6: 21687203 and no others for p < 80000000; if k = 7: 149, 43951591 and no others for p < 80000000; if k = 8: 31, 131 and no others for p < 80000000; if k = 9: 58691999 and no others for p < 80000000."
|
|
|
LINKS
| Hisanori Mishima, Factorization results for #Pn (Primorial) + 1
|
|
|
EXAMPLE
| 1 + Product of the primes < 19 = 1 + 2*3*5*7*11*13*17 = 510511 = 19*26869; so 19 is a term of the sequence.
|
|
|
MATHEMATICA
| p = 2; Do[q = Prime[n]; If[ IntegerQ[(p + 1)/q], Print[q]]; p = p*q, {n, 2, 86120} ]
|
|
|
PROG
| (PARI) a066735(m) =local(k, p); k=1; forprime(p=2, m, if((k+1)%p==0, print1(p, ", ")); k=k*p)
|
|
|
CROSSREFS
| Cf. A002110, A002585, A100465.
Sequence in context: A048827 A032077 A014547 * A099069 A038584 A108022
Adjacent sequences: A066732 A066733 A066734 * A066736 A066737 A066738
|
|
|
KEYWORD
| nonn
|
|
|
AUTHOR
| Joseph L. Pe (joseph_l_pe(AT)hotmail.com), Jan 15 2002
|
|
|
EXTENSIONS
| No further terms up to prime(216816) = 2999999. Is the sequence finite? - Klaus Brockhaus (klaus-brockhaus(AT)t-online.de), Jan 17 2002
No further terms up to 80000000. - Levai Gabor [L'{e}vai G'{a}bor], (gablevai(AT)vipmail.hu), Nov 23, 2004
|
| |
|
|
