A387590 a(n) is the first prime that is (product + sum) of 2*n consecutive primes.

11, 227, 30071, 3534749459194564381, 266186053068911, 1331590860773071703197, 78832548083496383033879927, 868535340156086171356445197408993, 396676631543316531327961869275231, 8902150522975861711854133933957, 9673689397457976659175106059313232036314768319

Offset

1,1

Comments

a(n) is the least prime of the form Product_{k=i..i+2*n-1} prime(k) + Sum_{k=i..i+2*n-1} prime(k).

Links

Robert Israel, Table of n, a(n) for n = 1..119

Example

For n = 4, a(4) = 191 * 193 * 197 * 199 * 211 * 223 * 227 * 229 + 191 + 193 + 197 + 199 + 211 + 223 + 227 + 229 = 3534749459194564381 is prime, where 191, ..., 229 are 8 consecutive primes, and no previous sequence of 8 consecutive primes works.

Maple

f:= proc(n) local L, v, i;
  L:= [seq(ithprime(i), i=1..2*n)];
  do
    v:= convert(L, `*`) + convert(L, `+`);
    if isprime(v) then return v fi;
    L:= [op(L[2..2*n]), nextprime(L[2*n])];
  od
end proc:
R:= seq(f(n), n=1..20);

Crossrefs

Cf. A390935.

Sequence in context: A347482 A170948 A245076 * A120850 A289716 A386864

Adjacent sequences: A387587 A387588 A387589 * A387591 A387592 A387593

Keyword

nonn

Author

Will Gosnell and Robert Israel, Nov 27 2025

Status

approved