A390935 a(n) is the first prime that is (product minus sum) of a sequence of 2*n consecutive primes.

7, 193, 29989, 1985383050388081, 100280244907, 1768926654228131160013897, 13082761331669749, 345838388442298632369626737513, 20752693410326487146559341738976742800539, 1253894832308423555527687468775077849, 8903838997318993853815253656003369523368299760147856304541019312543

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..115

Example

a(1) = 7 because 7 = 3*5 - (3+5) is prime where 3 and 5 are two consecutive primes, while 2*3 - (2+3) = 1 is not prime.

Maple

f:= proc(n) local L, i, v;
  L:= [seq(ithprime(i), i=1..2*n)]:
do
  v:= convert(L, `*`)-convert(L, `+`);
  if isprime(v) then return(v) fi;
  L:= [seq(L[i], i=2..2*n), nextprime(L[2*n])]
od:
end proc:
map(f, [$1..12]);

Crossrefs

Cf. A096345, A387590, A387946, A390916, A390933.

Sequence in context: A159826 A385066 A012849 * A308610 A277420 A220754

Adjacent sequences: A390932 A390933 A390934 * A390936 A390937 A390938

Keyword

nonn

Author

Will Gosnell and Robert Israel, Nov 24 2025

Status

approved