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Numbers n such that (product of first n primes)+1 is divisible by the (n+1)-th prime. Also n such that A075306(n)-1 is equal to A002110(n). Positions of 1 in A081617.
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%I #23 Oct 01 2020 08:39:06

%S 1,7,232,430

%N Numbers n such that (product of first n primes)+1 is divisible by the (n+1)-th prime. Also n such that A075306(n)-1 is equal to A002110(n). Positions of 1 in A081617.

%C a(5) is greater than 10^7. - _Matty Muir_, Oct 01 2020

%e The 8th prime, 19, divides 2*3*5*7*11*13*17+1=510511, thus 7 is a member.

%t With[{nn=500},Flatten[Position[Thread[{Rest[FoldList[Times,1,Prime[ Range[ nn]]]]+ 1, Prime[ Range[2,nn+1]]}],_?(Divisible[#[[1]],#[[2]]]&),{1},Heads->False]]] (* _Harvey P. Dale_, Apr 18 2015 *)

%o (PARI) p=1; for(n=1, 10^5, p=p*prime(n); if((p+1)%prime(n+1)==0, print1(n", ")))

%Y Cf. A066735.

%K nonn,hard,more

%O 1,2

%A _Ralf Stephan_, Mar 24 2003