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A319065
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..7, with k running over the positive integers; square array, read by antidiagonals, downwards.
7
126664001, 133487693, 230695118, 141313157, 633266299, 882345432, 236176001, 1221760151, 1986592318, 12106746963, 242883757, 1575527851, 2715632968, 12709975396, 93732236423, 356977349, 1881738424, 3726163057, 38456038702, 122728381675, 66888229817
OFFSET
1,1
EXAMPLE
The array starts as follows:
126664001, 133487693, 141313157, 236176001, 242883757, 356977349, 358254649
230695118, 633266299, 1221760151, 1575527851, 1881738424, 2118321224
882345432, 1986592318, 2715632968, 3726163057, 5229752849
12106746963, 12709975396, 38456038702, 66479920578
93732236423, 122728381675, 143904477566
66888229817, 79246182226
84391291750
MATHEMATICA
rows = 7; t = 7;
T = Table[lst = {}; b = 2;
While[Length[lst] < rows - n + 1,
fnd = True;
For[i = 0, i <= t, i++,
p = Prime[n + i];
If[PowerMod[b, (p - 1), p^2] != 1 , fnd = False; Break[]]];
If[fnd, 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, Oct 07 2019 *)
PROG
(PARI) printrow(n, terms) = my(c=0); for(b=2, oo, my(j=0); for(i=0, 7, my(p=prime(n+i)); if(Mod(b, p^2)^(p-1)==1, j++)); if(j==8, print1(b, ", "); c++); if(c==terms, break))
array(rows, cols) = for(x=1, rows, printrow(x, cols); print(""))
array(3, 3) \\ print initial 3 rows and 3 columns of array
CROSSREFS
Cf. analog for i = 0..t: A319059 (t=1), A319060 (t=2), A319061 (t=3), A319062 (t=4), A319063 (t=5), A319064 (t=6).
Sequence in context: A227274 A162450 A339537 * A344832 A334346 A115301
KEYWORD
nonn,tabl,more
AUTHOR
Felix Fröhlich, Sep 12 2018
EXTENSIONS
a(7)-a(21) from Robert Price, Oct 07 2019
STATUS
approved