A319061 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..3, with k running over the positive integers; square array, read by antidiagonals, downwards.

557, 901, 1207, 1549, 4607, 1451, 2449, 5176, 2774, 13543, 4049, 10124, 8201, 42269, 24675, 5293, 19601, 13543, 91110, 45124, 39016, 5849, 20924, 24482, 91678, 95236, 302947, 217682, 6193, 22049, 30949, 101399, 188872, 387587, 928423, 165407, 7057, 26018

Offset

1,1

Links

Table of n, a(n) for n=1..38.

Example

The array starts as follows:
     557,    901,    1549,    2449,    4049,    5293,    5849,    6193
    1207,   4607,    5176,   10124,   19601,   20924,   22049,   26018
    1451,   2774,    8201,   13543,   24482,   30949,   31457,   40199
   13543,  42269,   91110,   91678,  101399,  132576,  142148,  210258
   24675,  45124,   95236,  188872,  236915,  273971,  296449,  298117
   39016, 302947,  387587,  609436,  637111,  962525, 1015033, 1074751
  217682, 928423, 1546225, 1666084, 1756986, 2105290, 2673538, 2733520
  165407, 215029, 1008933, 1370816, 1487743, 1493395, 1624207, 2998943

Mathematica

rows = 8; t = 3;
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, 3, my(p=prime(n+i)); if(Mod(b, p^2)^(p-1)==1, j++)); if(j==4, 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), A319060 (t=2), A319062 (t=4), A319063 (t=5), A319064 (t=6), A319065 (t=7).

Sequence in context: A371879 A177331 A289564 * A339533 A344828 A260066

Adjacent sequences: A319058 A319059 A319060 * A319062 A319063 A319064

Keyword

nonn,tabl

Author

Felix Fröhlich, Sep 09 2018

Status

approved