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A326234 Numbers n such that N = n^3 is a twin rank (A002822: 6N +- 1 are twin primes). 8
1, 28, 42, 168, 203, 287, 308, 518, 1043, 1057, 1512, 1603, 1638, 1680, 1757, 1988, 2905, 3367, 3927, 4018, 4928, 5033, 5145, 5257, 5292, 5432, 5733, 6762, 7182, 7210, 7798, 8715, 10213, 10318, 10668, 10745, 11088, 12243, 13552, 14245, 14588, 14707, 15155, 15323, 15687, 15722, 15757 (list; graph; refs; listen; history; text; internal format)
OFFSET
1,2
COMMENTS
Dinculescu notes that when n^2 or n^3 is a twin rank > 1 (i.e., in A002822), then n is a multiple of 5, resp. 7. It is unknown whether there exist other pairs (a, b) different from (5, 2) and (7, 3) such that n^b => a | n. (Of course (5, 2k) and (7, 3k) and (35, 6k) is a solution for any k.) See A326233 for the terms > 1 divided by 7.
See A326232 and A326231 for the case n^2, A326236 and A326235 for n^6.
LINKS
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) = 7*A326233(n-1), n >= 2.
PROG
(PARI) select( is(n)=!for(s=1, 2, ispseudoprime(6*n^3+(-1)^s)||return), [1..10^5])
CROSSREFS
Cf. A002822, A326233 (a(n)/7, n>1), A326231, A326232 (analog for n^2), A326235, A326236 (analog for n^6), A326230 (least twin rank n^k > 1 for given k).
Sequence in context: A025359 A056031 A061826 * A260954 A349495 A169962
KEYWORD
nonn
AUTHOR
STATUS
approved

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Last modified July 13 02:50 EDT 2024. Contains 374265 sequences. (Running on oeis4.)