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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
OFFSET
1,1
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
KEYWORD
nonn,tabl
AUTHOR
Felix Fröhlich, Sep 09 2018
STATUS
approved