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%I #24 Feb 26 2024 01:26:03
%S 2,3,19,1471,3001
%N Primes p dividing 1 + the product of the primes less than p.
%C No further terms up to prime(216816) = 2999999. Is the sequence finite? - _Klaus Brockhaus_, Jan 17 2002
%C From Lévai Gábor (gablevai(AT)vipmail.hu), Nov 23 2004: (Start)
%C 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.
%C 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)
%C No further terms up to 80000000. - Lévai Gábor (gablevai(AT)vipmail.hu), Nov 23 2004
%C a(6) > 179424673 = prime(10^7). - _Giovanni Resta_, Apr 13 2017
%C a(6) > 914799232 > prime(46727379). - _Max Z. Scialabba_, Feb 26 2024
%H Hisanori Mishima, <a href="http://www.asahi-net.or.jp/~KC2H-MSM/mathland/matha1/matha102.htm">Factorization results for #Pn (Primorial) + 1</a>
%e 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.
%t p = 2; Do[q = Prime[n]; If[ IntegerQ[(p + 1)/q], Print[q]]; p = p*q, {n, 2, 86120} ]
%o (PARI) a066735(m) =local(k,p); k=1; forprime(p=2,m, if((k+1)%p==0,print1(p,",")); k=k*p)
%Y Cf. A002110, A002585, A100465, A081618.
%K nonn,more
%O 1,1
%A _Joseph L. Pe_, Jan 15 2002
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