A341238 Numbers k such that there do not exist consecutive primes (p,q) such that (2*k-q,2*k-p) are consecutive primes.

1, 2, 3, 7, 10, 13, 14, 16, 19, 20, 22, 25, 28, 29, 31, 35, 37, 40, 43, 44, 46, 47, 52, 58, 59, 61, 62, 65, 67, 73, 74, 79, 82, 83, 85, 88, 89, 91, 100, 103, 104, 106, 107, 119, 121, 124, 125, 127, 130, 133, 136, 139, 142, 145, 148, 149, 151, 163, 164, 166, 167, 172, 178, 179, 181, 182, 187, 188

Offset

1,2

Comments

Numbers k such that A341237(k) = 0.

Is the sequence finite? After a(351) = 12077 there are no other terms < 3*10^6.

Is 3 the only term divisible by 3?

Links

Robert Israel, Table of n, a(n) for n = 1..351

Example

a(4) = 7 is a term because for each of the consecutive prime pairs (p,q) = (2,3), (3,5), (5,7), (7,11), (11,13), the corresponding pairs (14-q,14-p) = (11,12), (9,11), (7,9), (3,7), (1,3) are not consecutive primes.

Maple

filter:= proc(n) local p, q, count;
  q:= 2: count:= 0:
  while q < 2*n -2 do
    p:= q; q:= nextprime(q);
    if isprime(2*n-p) and prevprime(2*n-p)=2*n-q then return false fi;
  od;
  true
end proc:
select(filter, [$1..200]);

Crossrefs

Cf. A341237.

Sequence in context: A171863 A101956 A273064 * A002238 A002255 A272649

Adjacent sequences: A341235 A341236 A341237 * A341239 A341240 A341241

Keyword

nonn

Author

J. M. Bergot and Robert Israel, Feb 07 2021

Status

approved