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A341238
Numbers k such that there do not exist consecutive primes (p,q) such that (2*k-q,2*k-p) are consecutive primes.
2
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
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
KEYWORD
nonn
AUTHOR
J. M. Bergot and Robert Israel, Feb 07 2021
STATUS
approved