OFFSET
1,1
COMMENTS
Similar sequence with odd integers d is A040976 \ {0}.
Terms are even numbers that are not divisible by 3 and that are not also in A206037.
These longest corresponding APs are of the form (q, q+d) with q odd primes (see examples).
This subsequence of A359408 corresponds to the second case '2 is one less than prime 3' (see A173919); the first case is linked to A040976.
A342309(d) gives the first element of the smallest such AP with 2 elements whose common difference is a(n) = d.
LINKS
FORMULA
EXAMPLE
d = 16 is a term because the first longest APs of primes with common difference 16 are (3, 19), (7,23), (13, 29), ... and all have 2 elements because next elements should be respectively 35, 39 and 45 that are all composite; the first such AP that starts with A342309(16) = 3 is (3, 19).
d = 22 is a term because the first longest APs of primes with common difference 22 are (7, 29), (19, 41), (31, 53), ... and all have 2 elements because next elements should be respectively 51, 63 and 75 that are all composite; the first such AP that starts with A342309(22) = 7 is (7, 29).
MAPLE
filter := d -> (irem(d, 2) = 0) and (irem(d, 3) <> 0) and not isprime(3+d) or isprime(3+d) and not isprime(3+2*d) : select(filter, [`$`(1 .. 270)]);
isA360735 := d -> isA047235(d) and not isA206037(d): # Peter Luschny, Mar 03 2023
MATHEMATICA
Select[Range[2, 270, 2], Mod[#, 3] > 0 && Nand @@ PrimeQ[{# + 3, 2*# + 3}] &] (* Amiram Eldar, Mar 03 2023 *)
PROG
(PARI) isok(d) = !(d%2) && (d%3) && !(isprime(d+3) && isprime(2*d+3)); \\ Michel Marcus, Mar 03 2023
CROSSREFS
KEYWORD
nonn
AUTHOR
Bernard Schott, Feb 19 2023
STATUS
approved