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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. 7
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 (list; table; graph; refs; listen; history; text; internal format)
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: A233355 A177331 A289564 * A339533 A260066 A105979

Adjacent sequences:  A319058 A319059 A319060 * A319062 A319063 A319064

KEYWORD

nonn,tabl

AUTHOR

Felix Fröhlich, Sep 09 2018

STATUS

approved

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Last modified May 6 09:45 EDT 2021. Contains 343580 sequences. (Running on oeis4.)