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 A282902 Square array A(n, k) read by antidiagonals downwards: multiplicative order of 2 modulo prime(n)^k, where k runs over the positive integers. 3
 2, 6, 4, 18, 20, 3, 54, 100, 21, 10, 162, 500, 147, 110, 12, 486, 2500, 1029, 1210, 156, 8, 1458, 12500, 7203, 13310, 2028, 136, 18, 4374, 62500, 50421, 146410, 26364, 2312, 342, 11, 13122, 312500, 352947, 1610510, 342732, 39304, 6498, 253, 28, 39366, 1562500, 2470629, 17715610, 4455516, 668168, 123462 (list; table; graph; refs; listen; history; text; internal format)
 OFFSET 2,1 COMMENTS The number of initial terms in row n with constant values is equal to the highest value of x such that p = prime(n) satisfies 2^(p-1) == 1 (mod p^x). From Robert Israel, Feb 24 2017: (Start) a(n,k+1) is either a(n,k) or a(n,k)*prime(n). If it is a(n,k)*prime(n), then a(n,k+j) = a(n,k)*prime(n)^j for all j>=1. a(n,2) = a(n,1) if and only if prime(n) is a Wieferich prime (A001220). (End) LINKS Robert Israel, Table of n, a(n) for n = 2..10012 (first 142 antidiagonals, flattened) EXAMPLE Array A(n, k) starts    2,   6,   18,     54,     162,      486,      1458    4,  20,  100,    500,    2500,    12500,     62500    3,  21,  147,   1029,    7203,    50421,    352947   10, 110, 1210,  13310,  146410,  1610510,  17715610   12, 156, 2028,  26364,  342732,  4455516,  57921708    8, 136, 2312,  39304,  668168, 11358856, 193100552   18, 342, 6498, 123462, 2345778, 44569782, 846825858 MAPLE seq(seq(numtheory:-order(2, ithprime(i)^(m-i)), i=2..m-1), m=2..10); # Robert Israel, Feb 24 2017 PROG (PARI) a(n, k) = znorder(Mod(2, prime(n)^k)) array(rows, cols) = for(n=2, rows+1, for(k=1, cols, print1(a(n, k), ", ")); print("")) array(7, 8) \\ print 7 X 8 array CROSSREFS Cf. A014664 (column 1), A243905 (column 2). Cf. A001220. Sequence in context: A098917 A054786 A269372 * A033457 A133936 A065350 Adjacent sequences:  A282899 A282900 A282901 * A282903 A282904 A282905 KEYWORD nonn,tabl,more AUTHOR Felix FrÃ¶hlich, Feb 24 2017 STATUS approved

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Last modified January 18 01:05 EST 2020. Contains 330995 sequences. (Running on oeis4.)