A319059 A(n, k) is the k-th number b > 1 such that b^(prime(n+i)-1) == 1 (mod prime(n+i)^2) for each i = 0..1, with k running over the positive integers; square array, read by antidiagonals, downwards.

17, 37, 26, 53, 82, 18, 73, 107, 68, 148, 89, 118, 99, 215, 239, 109, 143, 226, 362, 360, 249, 125, 199, 276, 606, 485, 577, 423, 145, 224, 293, 717, 596, 653, 653, 28, 161, 226, 324, 753, 606, 868, 2098, 784, 63, 181, 251, 374, 766, 699, 1520, 2526, 1921, 571

Offset

1,1

Links

Table of n, a(n) for n=1..54.

Example

The array starts as follows:
    17,   37,   53,    73,    89,   109,   125,   145,   161,   181,   197,   217
    26,   82,  107,   118,   143,   199,   224,   226,   251,   307,   332,   343
    18,   68,   99,   226,   276,   293,   324,   374,   393,   557,   607,   618
   148,  215,  362,   606,   717,   753,   766,  1207,  1304,  1322,  1371,  1451
   239,  360,  485,   596,   606,   699,   844,   846,   995,  1330,  1371,  1451
   249,  577,  653,   868,  1520,  1948,  1958,  2098,  2178,  2446,  2536,  2850
   423,  653, 2098,  2526,  2889,  3180,  4270,  4400,  4625,  4755,  5416,  5531
    28,  784, 1921,  2234,  2293,  3004,  4233,  4566,  4631,  4762,  4938,  5353
    63,  571, 1545,  3304,  3585,  3969,  4204,  5420,  6995,  7583,  7765,  7805
   374, 1492, 2509,  3323,  3405,  4472,  5651,  6154,  6492,  7805, 12348, 13040
   117, 1693, 2157,  4431,  4688,  6154,  6728,  6844,  6962,  9089, 11533, 13689
   787, 1368, 3214,  4106,  4895,  5552,  5830,  5900,  8892,  9229, 11389, 14272
  2059, 2152, 5548,  8354, 10557, 14368, 20320, 27657, 29296, 29945, 31434, 31452
  1085, 1771, 2210, 17902, 18793, 19679, 23670, 23676, 24298, 24928, 25885, 31800
   655, 1586, 1914,  3330,  3818,  7772,  8765,  9436,  9459, 12087, 13183, 24501

Mathematica

rows = 10; t = 1;
T = Table[lst = {}; b = 2;
   While[Length[lst] < rows,
    p = Prime[n + Range[0, t]];
    If[AllTrue[PowerMod[b, (p - 1), p^2], # == 1 &], AppendTo[lst, b]]; b++];
   lst, {n, rows}];
T // TableForm (* Print the A(n, k) table *)
Flatten[Table[T[[j, i - j + 1]], {i, 1, rows}, {j, 1, i}]] (* Robert Price, Sep 30 2019 *)

Prog

(PARI) printrow(n, terms) = my(c=0); for(b=2, oo, my(j=0); for(i=0, 1, my(p=prime(n+i)); if(Mod(b, p^2)^(p-1)==1, j++)); if(j==2, print1(b, ", "); c++); if(c==terms, break))
array(rows, cols) = for(x=1, rows, printrow(x, cols); print(""))
array(8, 10) \\ print initial 8 rows and 10 columns of array

Crossrefs

Cf. A244249, A256236, A259075 (column 1).

Cf. analog for i = 0..t: A319060 (t=2), A319061 (t=3), A319062 (t=4), A319063 (t=5), A319064 (t=6), A319065 (t=7).

Sequence in context: A116112 A190755 A098849 * A217195 A177835 A075698

Adjacent sequences: A319056 A319057 A319058 * A319060 A319061 A319062

Keyword

nonn,tabl

Author

Felix Fröhlich, Sep 09 2018

Status

approved