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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. 7
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 (list; table; graph; refs; listen; history; text; internal format)
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

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Last modified May 9 10:28 EDT 2021. Contains 343732 sequences. (Running on oeis4.)