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.

126664001, 133487693, 230695118, 141313157, 633266299, 882345432, 236176001, 1221760151, 1986592318, 12106746963, 242883757, 1575527851, 2715632968, 12709975396, 93732236423, 356977349, 1881738424, 3726163057, 38456038702, 122728381675, 66888229817

Offset

1,1

Links

Table of n, a(n) for n=1..21.

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 Fröhlich, Sep 12 2018

Extensions

a(7)-a(21) from Robert Price, Oct 07 2019

Status

approved