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A319060 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..2, with k running over the positive integers; square array, read by antidiagonals, downwards. 6
449, 557, 226, 593, 557, 1207, 649, 901, 1451, 606, 701, 1126, 2743, 1371, 3469, 757, 1207, 2774, 1451, 5938, 653, 793, 1243, 3657, 1667, 7624, 2098, 5649, 901, 1324, 4232, 2175, 11980, 4755, 10538, 26645, 1349, 1549, 4607, 2774, 12248, 5845, 11137, 35973 (list; table; graph; refs; listen; history; text; internal format)
OFFSET

1,1

LINKS

Table of n, a(n) for n=1..44.

EXAMPLE

The array starts as follows:

    449,   557,    593,    649,    701,    757,    793,    901,   1349,   1457

    226,   557,    901,   1126,   1207,   1243,   1324,   1549,   2224,   2449

   1207,  1451,   2743,   2774,   3657,   4232,   4607,   5176,   6682,   7251

    606,  1371,   1451,   1667,   2175,   2774,   4244,   8201,  13543,  13670

   3469,  5938,   7624,  11980,  12248,  13543,  17554,  20809,  23344,  24675

    653,  2098,   4755,   5845,  24314,  24675,  25876,  30270,  39016,  40133

   5649, 10538,  11137,  18049,  18710,  21426,  23158,  39016,  50902,  55134

  26645, 35973,  44710,  49556,  78991,  85972,  89283, 101540, 131466, 157641

   7805, 41854, 155349, 165407, 190906, 215029, 235210, 245586, 271376, 296832

   6154, 18488,  65788, 104520, 136463, 178863, 263429, 335829, 394854, 399254

MATHEMATICA

rows = 10; t = 2;

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, 2, my(p=prime(n+i)); if(Mod(b, p^2)^(p-1)==1, j++)); if(j==3, 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.

Cf. analog for i = 0..t: A319059 (t=1), A319061 (t=3), A319062 (t=4), A319063 (t=5), A319064 (t=6), A319065 (t=7).

Sequence in context: A107666 A020466 A142420 * A105376 A325083 A243402

Adjacent sequences:  A319057 A319058 A319059 * A319061 A319062 A319063

KEYWORD

nonn,tabl

AUTHOR

Felix Fröhlich, Sep 09 2018

STATUS

approved

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Last modified July 14 16:21 EDT 2020. Contains 335729 sequences. (Running on oeis4.)