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A326235 Numbers k such that N = (35k)^6 is a twin rank (A002822: 6N +- 1 are twin primes). 6
52, 74, 137, 159, 238, 242, 304, 306, 456, 478, 547, 701, 756, 988, 1059, 1186, 1218, 1243, 1378, 1705, 1976, 2426, 2596, 2844, 2952, 3216, 3263, 3360, 3632, 3692, 3762, 4094, 4364, 4603, 4689, 4858, 5003, 5177, 5287, 5361, 5426, 5999, 6054, 6285, 6347, 6417, 6457, 6639, 6862, 7269, 7500 (list; graph; refs; listen; history; text; internal format)
OFFSET
1,1
COMMENTS
Dinculescu notes that if N = m^2 > 1 is a twin rank (i.e., in A002822), then m is a multiple of 5, and if N = m^3 > 1, then m is a multiple of 7, cf. A326231 and A326233. Thus, when N = m^6, then m is a multiple of 35, and here we list these m/35.
See A326236 for the numbers m.
LINKS
A. Dinculescu and M. F. Hasler, 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) = A326236(n+1)/35.
PROG
(PARI) select( is(n)=!for(s=1, 2, ispseudoprime(6*(35*n)^6+(-1)^s)||return), [1..10^4])
CROSSREFS
Cf. A002822, A326231 (analog for m^2), A326232, A326233 (analog for m^3), A326234, A326236 ({1} U {35*a(n)}), A326230 (least twin rank m^n for given n).
Sequence in context: A039388 A043211 A043991 * A118148 A111173 A090793
KEYWORD
nonn
AUTHOR
EXTENSIONS
a(1..10^4) independently computed using Mathematica and PARI/GP, by A. D. and M. F. Hasler, Jun 19 2019
STATUS
approved

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Last modified July 13 15:08 EDT 2024. Contains 374284 sequences. (Running on oeis4.)