A358822 a(n) is the first number k such that there are exactly n pairs of primes p < q with p + q = k such that p*q - k and p*q + k are both prime.

2, 8, 48, 30, 114, 264, 390, 630, 1080, 660, 1470, 2046, 2730, 1680, 2310, 4530, 1650, 2760, 1290, 4170, 3150, 4590, 4440, 8610, 7800, 6090, 7950, 5040, 7560, 11550, 9690, 10530, 12180, 14280, 11520, 10920, 19980, 12810, 12210, 18270, 12390, 13230, 17460, 15990, 23070, 14490, 14880, 24540, 16830

Offset

0,1

Links

Table of n, a(n) for n=0..48.

Example

a(3) = 30 because for k = 30 there are exactly 3 such pairs:
  30 = 7 + 23 with 7*23 + 30 = 191 and 7*23 - 30 = 131 prime
  30 = 11 + 19 with 11*19 + 30 = 239 and 11*19 - 30 = 179 prime
  30 = 13 + 17 with 13*17 + 30 = 251 and 13*17 - 30 = 191 prime,
and 30 is the smallest number that works.

Maple

B:= Vector(10^5):
P:= select(isprime, [seq(i, i=3..10^5, 2)]):
nP:= nops(P):
for i from 1 to nP do
  for j from i+1 to nP do
    n:= P[i]+P[j];
    if n > 10^5 then break fi;
    if isprime(P[i]*P[j]+n) and isprime(P[i]*P[j]-n) then
      B[n]:= B[n]+1
    fi
od od:
W:= Array(0..max(B)):
for n from 2 to 10^5 by 2 do
if W[B[n]] = 0 then W[B[n]]:= n fi
od:
if not member(0, W, 'q') then q:= max(B)+1 fi;
convert(W[0..q-1], list);

Crossrefs

Sequence in context: A233337 A199136 A181413 * A003275 A253665 A078558

Adjacent sequences: A358819 A358820 A358821 * A358823 A358824 A358825

Keyword

nonn

Author

J. M. Bergot and Robert Israel, Dec 02 2022

Status

approved