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A321904
Irregular table read by rows: T(n,k) is the smallest m such that m^(-m) == 2*k + 1 (mod 2^n), 0 <= k <= 2^(n-1) - 1.
7
1, 1, 3, 1, 3, 5, 7, 1, 3, 13, 7, 9, 11, 5, 15, 1, 19, 29, 7, 25, 27, 21, 15, 17, 3, 13, 23, 9, 11, 5, 31, 1, 51, 29, 7, 57, 59, 21, 15, 49, 3, 13, 23, 41, 11, 5, 31, 33, 19, 61, 39, 25, 27, 53, 47, 17, 35, 45, 55, 9, 43, 37, 63
OFFSET
1,3
COMMENTS
The n-th row contains 2^(n-1) numbers, and is a permutation of the odd numbers below 2^n.
For all n, k we have v(T(n,k)-1, 2) = v(k, 2) + 1 and v(T(n,k)+1, 2) = v(k+1, 2) + 1, where v(k, 2) = A007814(k) is the 2-adic valuation of k.
For n >= 3, T(n,k) = 2*k + 1 iff k == -1 (mod 2^floor((n-1)/2)) or k = 0 or k = 2^(n-2).
T(n,k) is the multiplicative inverse of A321905(n,k) modulo 2^n.
FORMULA
T(n,k) = 2^n - A320562(n,2^(n-1)-1-k).
EXAMPLE
Table starts
1,
1, 3,
1, 3, 5, 7,
1, 3, 13, 7, 9, 11, 5, 15,
1, 19, 29, 7, 25, 27, 21, 15, 17, 3, 13, 23, 9, 11, 5, 31,
1, 51, 29, 7, 57, 59, 21, 15, 49, 3, 13, 23, 41, 11, 5, 31, 33, 19, 61, 39, 25, 27, 53, 47, 17, 35, 45, 55, 9, 43, 37, 63,
...
PROG
(PARI) T(n, k) = my(m=1); while(Mod(m, 2^n)^(-m)!=2*k+1, m+=2); m
tabf(nn) = for(n=1, nn, for(k=0, 2^(n-1)-1, print1(T(n, k), ", ")); print)
CROSSREFS
Cf. A007814.
{x^x} and its inverse: A320561 & A320562.
{x^(-x)} and its inverse: A321901 & this sequence.
{x^(1/x)} and its inverse: A321902 & A321905.
{x^(-1/x)} and its inverse: A321903 & A321906.
Sequence in context: A170898 A321901 A321906 * A321903 A189442 A320562
KEYWORD
nonn,tabf
AUTHOR
Jianing Song, Nov 21 2018
STATUS
approved