A355555 a(n) is the first prime prime(j) such that prime(j) + prime(k) + prime(k+1) is prime for k = j+1..j+n but not k = j+n+1.

2, 17, 5, 7, 53, 197, 848699, 2802313, 24281267, 54927644129, 29566753319

Offset

0,1

Comments

a(11) > 2*10^12. - Iain Fox, Jul 09 2022

Links

Table of n, a(n) for n=0..10.

Example

a(3) = 7 because 7+11+13 = 31, 7+13+17 = 37 and 7+17+19 = 41 are prime but 7+19+23 = 49 is not.

Maple

V:= Array(0..8): count:= 0:
f:= proc(n) local p, i;
       p:= ithprime(n);
       for i from 0 do
         if not isprime(p+ithprime(n+i+1)+ithprime(n+i+2)) then return i fi
       od
end proc:
for nn from 1 while count < 9 do
   v:= f(nn);
   if V[v] = 0 then V[v]:= ithprime(nn)   fi;
od:
convert(V, list);

Prog

(PARI) a(n) = my(pk, pk1); forprime(pj=2, oo, pk=nextprime(pj+1); for(x=0, n, pk1=nextprime(pk+1); if(!bitxor(x==n, isprime(pj+pk+pk1)), next(2)); pk=pk1); return(pj)) \\ Iain Fox, Jul 06 2022

Crossrefs

Cf. A000040.

Sequence in context: A144212 A186683 A210492 * A370111 A057280 A055677

Adjacent sequences: A355552 A355553 A355554 * A355556 A355557 A355558

Keyword

nonn,more,hard

Author

J. M. Bergot and Robert Israel, Jul 06 2022

Extensions

a(9)-a(10) from Iain Fox, Jul 06 2022

Status

approved