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 A066735 Primes p dividing 1 + the product of the primes less than p. 5
 2, 3, 19, 1471, 3001 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,1 COMMENTS No further terms up to prime(216816) = 2999999. Is the sequence finite? - Klaus Brockhaus, Jan 17 2002 From Lévai Gábor (gablevai(AT)vipmail.hu), Nov 23 2004: (Start) 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. (End) No further terms up to 80000000. - Lévai Gábor (gablevai(AT)vipmail.hu), Nov 23 2004 a(6) > 179424673 = prime(10^7). - Giovanni Resta, Apr 13 2017 a(6) > 914799232 > prime(46727379). - Max Z. Scialabba, Feb 26 2024 LINKS Table of n, a(n) for n=1..5. 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, A081618. Sequence in context: A048827 A032077 A014547 * A232498 A254380 A099069 Adjacent sequences: A066732 A066733 A066734 * A066736 A066737 A066738 KEYWORD nonn,more AUTHOR Joseph L. Pe, Jan 15 2002 STATUS approved

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Last modified June 12 18:04 EDT 2024. Contains 373359 sequences. (Running on oeis4.)