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A319061
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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.
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7
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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
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OFFSET
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1,1
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LINKS
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EXAMPLE
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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
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MATHEMATICA
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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 *)
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PROG
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(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
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CROSSREFS
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KEYWORD
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AUTHOR
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STATUS
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approved
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