A347866 a(n) is the least prime of the form 2*x+1 where x is the product of n consecutive primes.

3, 5, 13, 61, 421, 4621, 3233231, 333993639197596403, 2156564411, 5563815981553007, 200560490131, 401120980261, 39637878826194618534431695203503, 6120210247735371623457932152919, 6803741602666897883879, 12605609164720271524158527, 417378486395280242796047685872617741911685961999

Offset

0,1

Links

Robert Israel, Table of n, a(n) for n = 0..201

Example

a(6) = 2*(5*7*11*13*17*19)+1 = 3233231 because that is prime while 2*(2*3*5*7*11*13)+1 = 60061 and 2*(3*5*7*11*13*17)+1 = 510511 are not prime.

Maple

f:= proc(n) local P, i, r;
  P:= mul(ithprime(i), i=1..n);
  for i from 1 do
    r:= 2*P+1;
    if isprime(r) then return r fi;
    P:= P/ithprime(i)*ithprime(i+n);
  od
end proc:
map(f, [$0..20]);

Mathematica

a[n_] := Module[{x = Product[Prime[i], {i, 1, n}], p1 = 2, p2 = Prime[n + 1]}, While[! PrimeQ[2*x + 1], x *= (p2/p1); p1 = NextPrime[p1]; p2 = NextPrime[p2]]; 2*x + 1]; Array[a, 17, 0] (* Amiram Eldar, Jan 25 2022 *)

Crossrefs

Cf. A348430.

Sequence in context: A243161 A153207 A144718 * A066141 A159293 A051901

Adjacent sequences: A347863 A347864 A347865 * A347867 A347868 A347869

Keyword

nonn

Author

J. M. Bergot and Robert Israel, Jan 25 2022

Status

approved