A307818 Numbers k such that A240718(k) = 0.

1, 2, 3, 4, 5, 6, 9, 12, 15, 19, 49, 61, 63, 64, 110, 151, 154, 166, 173, 244, 278, 427, 454, 481, 496, 572, 575, 637, 677, 680, 681, 691, 704, 712, 766, 884, 928, 964, 1039, 1094, 1100, 1219, 1256, 1265, 1309, 1321, 1729, 1909, 1924, 2309, 2443, 2686, 2989, 3001, 3004, 3713, 4798, 4801, 5134, 5311, 5719, 5821, 6443, 6574, 6781, 7099, 7339, 8251, 9454, 10684, 11416, 11713, 11728, 21766, 27122, 31637

Offset

1,2

Comments

k is in the sequence if there are no primes p < sqrt(2*k-2) such that 2*k-p is prime.

There are no other terms < 10^7.

Conjecture: 31637 is the last term.

Links

Table of n, a(n) for n=1..76.

Example

a(7)=9 is in the sequence because the primes < sqrt(2*9-2)=4 are 2 and 3, and neither 2*9-2=16 nor 2*9-3=15 is prime.

Maple

P:= NULL: Res:= 1:  nextp:= 2:
for n from 2 to 10^6 do
  while nextp^2 < 2*n-2 do
   P:= P, nextp;
   nextp:= nextprime(nextp);
  od;
  if andmap(t -> not isprime(2*n-t), [P]) then
   Res:= Res, n
  fi;
od:
Res;

Crossrefs

Cf. A240718.

Sequence in context: A008813 A133463 A187550 * A358033 A057492 A178715

Adjacent sequences: A307815 A307816 A307817 * A307819 A307820 A307821

Keyword

nonn

Author

Robert Israel, Apr 30 2019

Status

approved