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A323555
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Irregular table read by rows: T(n,k) = (2*k+1)^(1/5) mod 2^n, 0 <= k <= 2^(n-1) - 1.
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4
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1, 1, 3, 1, 3, 5, 7, 1, 3, 5, 7, 9, 11, 13, 15, 1, 19, 21, 7, 9, 27, 29, 15, 17, 3, 5, 23, 25, 11, 13, 31, 1, 19, 21, 39, 41, 59, 61, 15, 17, 35, 37, 55, 57, 11, 13, 31, 33, 51, 53, 7, 9, 27, 29, 47, 49, 3, 5, 23, 25, 43, 45, 63, 1, 83, 21, 103, 105, 59, 125, 79, 81, 35, 101, 55, 57, 11, 77, 31, 33, 115, 53, 7, 9, 91, 29, 111, 113, 67, 5, 87, 89, 43, 109, 63
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OFFSET
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1,3
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COMMENTS
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T(n,k) is the unique x in {1, 3, 5, ..., 2^n - 1} such that x^5 == 2*k + 1 (mod 2^n).
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.
T(n,k) is the multiplicative inverse of A323554(n,k) modulo 2^n.
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LINKS
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EXAMPLE
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Table starts
1,
1, 3,
1, 3, 5, 7,
1, 3, 5, 7, 9, 11, 13, 15,
1, 19, 21, 7, 9, 27, 29, 15, 17, 3, 5, 23, 25, 11, 13, 31,
1, 19, 21, 39, 41, 59, 61, 15, 17, 35, 37, 55, 57, 11, 13, 31, 33, 51, 53, 7, 9, 27, 29, 47, 49, 3, 5, 23, 25, 43, 45, 63,
...
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PROG
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(PARI) T(n, k) = if(n==2, 2*k+1, lift(sqrtn(2*k+1+O(2^n), 5)))
tabf(nn) = for(n=1, nn, for(k=0, 2^(n-1)-1, print1(T(n, k), ", ")); print)
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CROSSREFS
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KEYWORD
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nonn,tabf
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AUTHOR
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STATUS
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approved
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