OFFSET
1,1
COMMENTS
The 6 elements are not necessarily consecutive primes.
A342309(d) gives the first element of the smallest AP with 6 elements whose common difference is a(n) = d.
LINKS
Diophante, A1880. NP en PA (prime numbers in arithmetic progression) (in French).
Wikipedia, Primes in arithmetic progression.
FORMULA
m is a term iff A123556(m) = 6.
EXAMPLE
d = 30 is a term because the longest possible APs of primes with common difference d = 30 all have 6 elements; the first such APs start with 7, 107, 359, .... The smallest one is (7, 37, 67, 97, 127, 157); then 187 = 11*17.
d = 60 is another term because the longest possible APs of primes with common difference d = 60 all have 6 elements; the first such APs start with 11, 53, 641, .... The smallest one is (11, 71, 131, 191, 251, 311); then 371 = 7*53.
d = 150 is not a term because the longest possible AP of primes with common difference d = 150 is (7, 157, 307, 457, 607, 757, 907) which has 7 elements; this last one is unique.
MAPLE
filter := d -> (irem(d, 30) = 0) and (irem(d, 7) <> 0) and not (isprime(7+d) and isprime(7+2*d) and isprime(7+3*d) and isprime(7+4*d) and isprime(7+5*d) and isprime(7+6*d)): select(filter, [$(1 .. 1740)]);
CROSSREFS
KEYWORD
nonn
AUTHOR
Bernard Schott, Jan 29 2023
STATUS
approved