A088411 A088257 indexed by A002110.

0, 1, 2, 3, 4, 5, 6, 11, 13, 24, 66, 68, 75, 167, 171, 172, 287, 310, 352, 384, 457, 564, 590, 616, 620, 643, 849, 1391, 1552, 1613, 1849, 2122, 2647, 2673, 4413, 13494, 31260, 33237, 67132, 85586, 234725

Offset: 1

Author

Ray Chandler, Sep 29 2003

Keywords

• nonn
• more

Comments

Union of A057704 and A014545. - Jeppe Stig Nielsen, Aug 01 2019

Examples

			3 is in the sequence because primorial p_3# = 2 * 3 * 5 = 30 has two prime neighbors 29 and 31.
4 is in the sequence because primorial p_4# = 2 * 3 * 5 * 7 = 210 has one prime neighbor 211; 209 = 11 * 19.
7 is not in the sequence because the product of the smallest 7 primes has two composite neighbors.
		

Crossrefs

Cf. A002110, A088257, A014545, A057704.

Programs

Maple

A:= NULL:
P:= 1: p:= 1;
for n from 1 to 700 do
  p:= nextprime(p);
  P:= P*p;
  if isprime(P+1) or isprime(P-1) then A:= A, n fi
od:
A; # Robert Israel, Aug 03 2016

Mathematica

Select[Range[0, 600], Total@ Boole@ PrimeQ@ {# - 1, # + 1} > 0 &@ Apply[Times, Prime@ Range@ #] &] (* Michael De Vlieger, Aug 03 2016 *)

PARI

is(k)=pr=prod(j=1,k,prime(j));ispseudoprime(pr-1)||ispseudoprime(pr+1) \\ Jeppe Stig Nielsen, Aug 01 2019

Formula

a(n)=k such that A088257(n)=A002110(k).

Extensions

a(22)-a(27) from Michael De Vlieger, Aug 03 2016

a(28)-a(40) from Jeppe Stig Nielsen, Aug 01 2019

a(41) from Jeppe Stig Nielsen, Oct 19 2021