A389369 Least prime starting a run of 2*n consecutive primes whose product minus sum is prime.

3, 2, 2, 67, 3, 79, 2, 41, 131, 29, 1033, 367, 61, 29, 271, 281, 43, 181, 191, 101, 653, 419, 569, 5827, 1627, 383, 131, 277, 547, 167, 709, 2477, 8069, 137, 2789, 733, 599, 659, 6197, 641, 691, 4793, 571, 911, 1163, 2347, 8017, 613, 2819, 149, 421, 5147, 887, 3631

Offset

1,1

Links

Table of n, a(n) for n=1..54.

Example

a(1) = 3 is a term because 3, 5 are 2 consecutive primes with (3*5) - (3+5) = 15 - 8 = 7 and 7 is 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(L[1]) fi;
  L:= [seq(L[i], i=2..2*n), nextprime(L[2*n])]
od:
end proc:
map(f, [$1..100]); # Robert Israel, Dec 02 2025

Mathematica

p[m_, n_]:=Product[Prime[j], {j, m, m+2n-1}]; s[m_, n_]:=Sum[Prime[j], {j, m, m+2n-1}]; a[n_]:=Module[{k=1}, While[!PrimeQ[p[k, n]-s[k, n]], k++]; Prime[k]]; Array[a, 54] (* James C. McMahon, Dec 12 2025 *)

Prog

(PARI) isok(n, ip) = my(v2=primes(2*n+ip-1), v1=primes(ip-1), vr=setminus(v2, v1)); isprime(vecprod(vr)-vecsum(vr));
a(n) = my(ip=1); while (!isok(n, ip), ip++); prime(ip); \\ Michel Marcus, Dec 02 2025

Crossrefs

Cf. A000040, A002110, A007504, A096345, A390916, A390917, A390918, A390935, A390933.

Sequence in context: A108032 A053370 A016458 * A372345 A058513 A319650

Adjacent sequences: A389366 A389367 A389368 * A389370 A389371 A389372

Keyword

nonn

Author

Jean-Marc Rebert, Dec 01 2025

Status

approved