A326229 Square array T(n,k) where row n >= 1 lists numbers m > 1 such that 6*m^n +- 1 are twin primes; read by falling antidiagonals.

2, 3, 5, 5, 10, 28, 7, 35, 42, 70, 10, 60, 168, 75, 2, 12, 70, 203, 80, 40, 1820, 17, 75, 287, 175, 208, 2590, 110, 18, 210, 308, 485, 425, 4795, 123, 1850, 23, 240, 518, 850, 873, 5565, 192, 3815, 2520, 25, 385, 1043, 970, 1608, 8330, 462, 5840, 5432, 220, 30, 430, 1057, 1255, 1713, 8470, 948, 6270, 6020, 560, 2023, 32

Offset

1,1

Comments

We assume that all rows have infinite length, in case this should not be the case we would fill the row with 0's after the last term.

From [Dinculescu] we know that whenever 2|n or 3|n, then all terms of row n are multiples of 5 resp. of 7 (where | means "divides"), cf. A326231 - A326234. We do not know other (independent) pairs (a, b) such that (m^b in A002822) implies a|m.

Links

Table of n, a(n) for n=1..67.

A. Dinculescu, On the Numbers that Determine the Distribution of Twin Primes, Surveys in Mathematics and its Applications, 13 (2018), 171-181.

Example

The array starts:
[   2     3     5     7    10    12    17    18   ...] = A002822 \ {1}
[   5    10    35    60    70    75   210   240   ...] = A326232 \ {1}
[  28    42   168   203   287   308   518  1043   ...] = A326234 \ {1}
[  70    75    80   175   485   850   970  1255   ...]
[   2    40   208   425   873  1608  1713  1718   ...]
[1820  2590  4795  5565  8330  8470 10640 10710   ...] = A326236 \ {1}
[ 110   123   192   462   948  1242  1255  1747   ...]
[1850  3815  5840  6270  8075  8960  9210 10420   ...]
[2520  5432  6020 10535 24017 29092 29295 29967   ...]
(...)
Column 1 is A326230(n): smallest m > 1 such that m^n is in A002822 (twin ranks).

Prog

(PARI) A326229_row(n, LENGTH=20)={my(g=5^!(n%2)*7^!(n%3), m=max(g, 2)-g); vector(LENGTH, i, while(m+=g, for(s=1, 2, ispseudoprime(6*m^n+(-1)^s)||next(2)); break); m)}

Crossrefs

Cf. A002822, A326230, A326231, ..., A326236.

Sequence in context: A368085 A265546 A066911 * A326187 A071850 A092749

Adjacent sequences: A326226 A326227 A326228 * A326230 A326231 A326232

Keyword

nonn,tabl

Author

M. F. Hasler, Jun 16 2019

Status

approved