OFFSET
1,1
COMMENTS
Dinculescu notes that if m^3 > 1 is a twin rank (i.e., in A002822), then m is always a multiple of 7. (Indeed, 6m^3 + 1 == 0 (mod 7) if m == 1, 2 or 4 (mod 7), and 6m^3 - 1 == 0 (mod 7) for m == 3, 5 or 6 (mod 7).)
He asks whether there are other pairs (a, b) different from (5, 2) and (7, 3) such that all twin ranks m^b > 1 are of the form m = a*n. (Of course (5, 2) and (7, 3) imply that (5, 2k), (7, 3k) and (35, 6k) is also such a pair for any k >= 1.)
This sequence lists these m/7 for (a, b) = (7, 3), see A326234 for the numbers m.
LINKS
Robert Israel, Table of n, a(n) for n = 1..10000
A. Dinculescu, On the Numbers that Determine the Distribution of Twin Primes, Surveys in Mathematics and its Applications, 13 (2018), 171-181.
FORMULA
a(n) = A326234(n+1)/7.
MAPLE
filter:= proc(n) local m;
m:= (7*n)^3;
isprime(6*m+1) and isprime(6*m-1)
end proc:
select(filter, [$1..3000]); # Robert Israel, Jun 17 2019
PROG
(PARI) select( is(n)=!for(s=1, 2, ispseudoprime(6*(7*n)^3+(-1)^s)||return), [1..10^4])
CROSSREFS
KEYWORD
nonn
AUTHOR
M. F. Hasler and Antonie Dinculescu, Jun 14 2019
STATUS
approved