A387687 a(n) is the smallest prime p greater than all previous terms such that the product of the previous terms plus p is prime.

2, 3, 5, 7, 13, 19, 23, 31, 41, 61, 67, 127, 197, 257, 277, 311, 331, 563, 653, 709, 719, 823, 1031, 1103, 1163, 1327, 1471, 1723, 1811, 1879, 1931, 1973, 2447, 2633, 2707, 2927, 3119, 3253, 3701, 4409, 4787, 5167, 5749, 6121, 6133, 6359, 7039, 7103, 7331, 7963

Offset

0,1

Comments

The presence of the even prime 2 makes this sequence work. a(0) = 2 since the empty product is 1 and 1 + 2 = 3 is a prime.

Links

Table of n, a(n) for n=0..49.

Example

2 + 3 = 5 (a prime).
2 * 3 + 5 = 11 (a prime).
2 * 3 * 5 * 7 * 13 * 19 + 23 = 51893 (a prime).
2 * 3 * 5 * 7 * 13 * 19 * 23 * 31 * 41 * 61 + 67 = 92495258377 (a prime).

Maple

x := 1: for i to 1010 do if isprime(x+ithprime(i)) then x := x*ithprime(i); printf("%d, ", ithprime(i)) end if; end do;

Mathematica

x = 1; p = {}; For[i = 1, i < 1010, i++, If[PrimeQ[x + Prime[i]], x *= Prime[i]; p = Append[p, Prime[i]]]]; p

Prog

(PARI) my(x=1); forprime(p=2, 8000, if(isprime(x+p), x*=p; print1(p, ", ")))

Crossrefs

Cf. A000040 (primes).

Sequence in context: A330968 A153591 A038917 * A385504 A124661 A385503

Adjacent sequences: A387684 A387685 A387686 * A387688 A387689 A387690

Keyword

nonn

Author

Michal Paulovic, Sep 05 2025

Status

approved