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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.

%I A326229 #13 Jan 17 2020 10:45:50
%S A326229 2,3,5,5,10,28,7,35,42,70,10,60,168,75,2,12,70,203,80,40,1820,17,75,
%T A326229 287,175,208,2590,110,18,210,308,485,425,4795,123,1850,23,240,518,850,
%U A326229 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
%N 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.
%C A326229 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.
%C A326229 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.
%H A326229 A. Dinculescu, <a href="http://www.utgjiu.ro/math/sma/v13/p13_11.pdf">On the Numbers that Determine the Distribution of Twin Primes</a>, Surveys in Mathematics and its Applications, 13 (2018), 171-181.
%e A326229 The array starts:
%e A326229 [   2     3     5     7    10    12    17    18   ...] = A002822 \ {1}
%e A326229 [   5    10    35    60    70    75   210   240   ...] = A326232 \ {1}
%e A326229 [  28    42   168   203   287   308   518  1043   ...] = A326234 \ {1}
%e A326229 [  70    75    80   175   485   850   970  1255   ...]
%e A326229 [   2    40   208   425   873  1608  1713  1718   ...]
%e A326229 [1820  2590  4795  5565  8330  8470 10640 10710   ...] = A326236 \ {1}
%e A326229 [ 110   123   192   462   948  1242  1255  1747   ...]
%e A326229 [1850  3815  5840  6270  8075  8960  9210 10420   ...]
%e A326229 [2520  5432  6020 10535 24017 29092 29295 29967   ...]
%e A326229 (...)
%e A326229 Column 1 is A326230(n): smallest m > 1 such that m^n is in A002822 (twin ranks).
%o A326229 (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)}
%Y A326229 Cf. A002822, A326230, A326231, ..., A326236.
%K A326229 nonn,tabl
%O A326229 1,1
%A A326229 _M. F. Hasler_, Jun 16 2019