A119411 -id:A119411 - cp's OEIS frontend

A088256 Primorial numbers k such that both k-1 and k+1 are prime.

6, 30, 2310

Offset: 1

Amarnath Murthy, Sep 27 2003

Conjecture: sequence is finite.
No more terms in the first 300 primorials. - David Wasserman, Jul 25 2005
Search extended to first 700 primorials by Michael De Vlieger, Aug 31 2016
Intersection of A014574 and A002110. - Michel Marcus, Dec 03 2016
Search extended to first 3000 primorials. - Josey Stevens, Aug 10 2021
The first more than 230000 primorial numbers k have been checked for whether k-1 or k+1 or both are primes. See links. If another term k exists, it is over about 10^1400000. - Jeppe Stig Nielsen, Oct 19 2021

			210 = primorial(4) is not a member as 209 is composite.

Chris K. Caldwell, The Top Twenty: Primorial, in the Prime Pages.
PrimeGrid, PRPNet: Primorial Prime Search - Server Statistics.

Cf. A001097, A002110, A088257, A014574, A119411, A136349.

f:= proc(n)
  local P;
  P:= mul(seq(ithprime(i),i=1..n));
  if isprime(P+1) and isprime(P-1) then P else NULL fi
end proc:
map(f, [$1..300]); # Robert Israel, Aug 31 2016

Select[Times @@ # & /@ Prime@ Range@ Range@ 700, Times @@ Boole@ PrimeQ@ {# - 1, # + 1} == 1 &] (* Michael De Vlieger, Aug 31 2016 *)
Select[FoldList[Times,Prime[Range[20]]],AllTrue[#+{1,-1},PrimeQ]&] (* Harvey P. Dale, Mar 31 2023 *)

lista(nn) = for (n=1, nn, pr = prod(i=1, n, prime(i)); if (isprime(pr-1) && isprime(pr+1), print1(pr, ", "))); \\ Michel Marcus, Aug 31 2016

Corrected by Ray Chandler, Sep 28 2003

A123376 Sum of the first s(n) primes, where s(n) is the sum of the first p(n) primes, where p(n) is the n-th prime. Note that s(n) is A022094.

Original entry on oeis.org

28, 129, 1371, 7141, 68341, 163541, 624211, 1086557, 2756043, 8546951, 11791577, 28122767, 46308119, 58262037, 88870153, 158512433, 263952799, 308206649, 480993245, 635060975, 724715753, 1053143991, 1331063769, 1845563079, 2750645663, 3325653577, 3650662901, 4369224195, 4767074983, 5637335441

Offset: 1

Peter C. Heinig (algorithms(AT)gmx.de), Oct 13 2006

			a(1)=28=2+3+5+7+11, since s(1)=5=2+3, since p(1)=2.

Cf. A119411, A022094.

for j from 1 to 23 do s[j]:=sum(ithprime(i), i=1..ithprime(j)); od; for j from 1 to 23 do sum(ithprime(i), i=1..s[j]); od;

With[{prs=Prime[Range[50000]]},Table[Total[Take[prs,Total[Take[prs, prs[[n]]]]]],{n,30}]] (* Harvey P. Dale, May 16 2012 *)

More terms from Robert Israel, Jul 30 2020

cp's OEIS Frontend

A088256 Primorial numbers k such that both k-1 and k+1 are prime.

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