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%I #22 Oct 21 2021 01:14:39
%S 0,1,2,3,4,5,6,11,13,24,66,68,75,167,171,172,287,310,352,384,457,564,
%T 590,616,620,643,849,1391,1552,1613,1849,2122,2647,2673,4413,13494,
%U 31260,33237,67132,85586,234725
%N A088257 indexed by A002110.
%C Union of A057704 and A014545. - _Jeppe Stig Nielsen_, Aug 01 2019
%F a(n)=k such that A088257(n)=A002110(k).
%e 3 is in the sequence because primorial p_3# = 2 * 3 * 5 = 30 has two prime neighbors 29 and 31.
%e 4 is in the sequence because primorial p_4# = 2 * 3 * 5 * 7 = 210 has one prime neighbor 211; 209 = 11 * 19.
%e 7 is not in the sequence because the product of the smallest 7 primes has two composite neighbors.
%p A:= NULL:
%p P:= 1: p:= 1;
%p for n from 1 to 700 do
%p p:= nextprime(p);
%p P:= P*p;
%p if isprime(P+1) or isprime(P-1) then A:= A, n fi
%p od:
%p A; # _Robert Israel_, Aug 03 2016
%t Select[Range[0, 600], Total@ Boole@ PrimeQ@ {# - 1, # + 1} > 0 &@ Apply[Times, Prime@ Range@ #] &] (* _Michael De Vlieger_, Aug 03 2016 *)
%o (PARI) is(k)=pr=prod(j=1,k,prime(j));ispseudoprime(pr-1)||ispseudoprime(pr+1) \\ _Jeppe Stig Nielsen_, Aug 01 2019
%Y Cf. A002110, A088257, A014545, A057704.
%K nonn,more
%O 1,3
%A _Ray Chandler_, Sep 29 2003
%E a(22)-a(27) from _Michael De Vlieger_, Aug 03 2016
%E a(28)-a(40) from _Jeppe Stig Nielsen_, Aug 01 2019
%E a(41) from _Jeppe Stig Nielsen_, Oct 19 2021
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