A119752 a(1)=2; a(n)=first even number greater than a(n-1) such that a(i)+a(n)+1 is prime for all i=1,2,...,n.

2, 8, 14, 44, 224, 638, 1274, 4004, 675404, 2203958, 3075158, 6195234164, 77989711184, 4566262987328

Offset: 1

Author

Walter Kehowski, Jun 17 2006

Keywords

• nonn
• more
• hard

Crossrefs

Cf. A119751.

Programs

Maple

R:= [2]: count:= 1:
for k from 4 by 2 while count < 11 do
  if isprime(2*k+1) and andmap(isprime, [seq(R[i]+k+1,i=1..count)]) then
     R:= [op(R),k]; count:= count+1
  fi
od:
R; # Robert Israel, Mar 06 2023

Mathematica

Table[If[n == 1, a[1] = 2, j = a[n - 1] + 2; While[a[n] = j; !
    AllTrue[Table[a[i] + a[n] + 1, {i, 1, n}], PrimeQ], j += 2]; j]
, {n, 1, 9}] (* Robert Price, Apr 03 2019 *)

PARI

isok(va, k, n) = if (isprime(2*k+1), for (i=1, n-1, if (! isprime(va[i]+k+1), return(0))); return(1));
lista(nn) = my(va=vector(nn)); va[1]=2; for (n=2, nn, my(k=va[n-1]+2); while (!isok(va, k, n), k+=2); va[n] = k); va; \\ Michel Marcus, Mar 06 2023

Extensions

a(13)-a(14) from Donovan Johnson, Mar 23 2008