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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 (list; table; graph; refs; listen; history; text; internal format)
 OFFSET 1,1 LINKS 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. A244249, A256236. 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 Adjacent sequences:  A319062 A319063 A319064 * A319066 A319067 A319068 KEYWORD nonn,tabl,more AUTHOR Felix FrÃ¶hlich, Sep 12 2018 EXTENSIONS a(7)-a(21) from Robert Price, Oct 07 2019 STATUS approved

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Last modified June 21 10:09 EDT 2021. Contains 345360 sequences. (Running on oeis4.)