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CONJECTURES INVOLVING ARITHMETICAL SEQUENCES
"... Abstract. We pose thirty conjectures on arithmetical sequences, most of which are about monotonicity of sequences of the form ( n √ an)n�1 or the form ( n+1 √ an+1 / n √ an)n�1, where (an)n�1 is a numbertheoretic or combinatorial sequence of positive integers. This material might stimulate further ..."
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Cited by 15 (6 self)
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Abstract. We pose thirty conjectures on arithmetical sequences, most of which are about monotonicity of sequences of the form ( n √ an)n�1 or the form ( n+1 √ an+1 / n √ an)n�1, where (an)n�1 is a numbertheoretic or combinatorial sequence of positive integers. This material might stimulate further
An uncertainty principle for arithmetic sequences
, 2004
"... Analytic number theorists usually seek to show that sequences which appear naturally in arithmetic are “welldistributed ” in some appropriate sense. In various discrepancy problems, combinatorics researchers have analyzed limitations to equidistribution, as have Fourier analysts when working with ..."
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Cited by 8 (3 self)
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Analytic number theorists usually seek to show that sequences which appear naturally in arithmetic are “welldistributed ” in some appropriate sense. In various discrepancy problems, combinatorics researchers have analyzed limitations to equidistribution, as have Fourier analysts when working
ARITHMETIC SEQUENCES AND FIBONACCI QUADRATICS
, 1989
"... It is known [1] that the equation Fnx 2 + Fn+iX Fn + 2 = 0 has solutions1 and Fn + 2/Fns where {Fn}n> 1 denotes the Fibonacci sequence. One wonders if other interesting results might be obtained if the coefficients of the quadratic equation were some other functions of the Fibonacci numbers. Th ..."
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It is known [1] that the equation Fnx 2 + Fn+iX Fn + 2 = 0 has solutions1 and Fn + 2/Fns where {Fn}n> 1 denotes the Fibonacci sequence. One wonders if other interesting results might be obtained if the coefficients of the quadratic equation were some other functions of the Fibonacci numbers. The
COVERING THE INTEGERS BY ARITHMETIC SEQUENCES II
 TRANS. AMER. MATH. SOC. 348(1996), NO. 11, 4279–4320
, 1996
"... Let A = {as + nsZ} k s=1 (n1 � · · · � nk) be a system of arithmetic sequences where a1, · · · , ak ∈ Z and n1, · · · , nk ∈ Z +. For m ∈ Z + system A will be called an (exact) mcover of Z if every integer is covered by A at least (exactly) m times. In this paper we reveal further connec ..."
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Let A = {as + nsZ} k s=1 (n1 � · · · � nk) be a system of arithmetic sequences where a1, · · · , ak ∈ Z and n1, · · · , nk ∈ Z +. For m ∈ Z + system A will be called an (exact) mcover of Z if every integer is covered by A at least (exactly) m times. In this paper we reveal further
On numerical semigroups generated by generalized arithmetic sequences
 Comm. Alg
"... Abstract. Given a numerical semigroup S, let M(S) = S \{0} and (lM(S)− lM(S)) = {x ∈ N0: x + lM(S) ⊆ lM(S)}. Define associated numerical semigroups B(S): = (M(S) − M(S)) and L(S): = ∪ ∞ l=1 (lM(S) − lM(S)). Set B0(S) = S, and for i ≥ 1, define Bi(S): = B(Bi−1(S)). Similarly, set L0(S) = S, and ..."
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Cited by 4 (2 self)
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(S) ⊆ Li(S) for all i ≥ 0. In this paper, we prove that if S is a numerical semigroup with a set of generators that form a generalized arithmetic sequence, then Bi(S) ⊆ Li(S) for all i ≥ 0. Moreover, we see that this containment is not necessarily satisfied if a set of generators of S form an almost
ON SOME CONJECTURES ON THE MONOTONICITY OF SOME ARITHMETICAL SEQUENCES ∗
, 2012
"... Here, we prove some conjectures on the monotony of combinatorial and number– theoretical sequences from a recent paper of Zhi–Wei Sun. ..."
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Here, we prove some conjectures on the monotony of combinatorial and number– theoretical sequences from a recent paper of Zhi–Wei Sun.
A NEW POLYNOMIALTIME ALGORITHM FOR LINEAR PROGRAMMING
 COMBINATORICA
, 1984
"... We present a new polynomialtime algorithm for linear programming. In the worst case, the algorithm requires O(tf'SL) arithmetic operations on O(L) bit numbers, where n is the number of variables and L is the number of bits in the input. The running,time of this algorithm is better than the ell ..."
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Cited by 860 (3 self)
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We present a new polynomialtime algorithm for linear programming. In the worst case, the algorithm requires O(tf'SL) arithmetic operations on O(L) bit numbers, where n is the number of variables and L is the number of bits in the input. The running,time of this algorithm is better than
Strongly sufficient sets and the distribution of arithmetic sequences in the 3x+1 graph
 DISCRETE MATHEMATICS 313
, 2014
"... The 3x+ 1 Conjecture asserts that the Torbit of every positive integer contains 1, where T maps x 7 → x/2 for x even and x 7 → (3x + 1)/2 for x odd. A set S of positive integers is sufficient if the orbit of each positive integer intersects the orbit of some member of S. In [9] it was shown that ev ..."
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Cited by 1 (0 self)
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that every arithmetic sequence is sufficient. In this paper we further investigate the concept of sufficiency. We construct sufficient sets of arbitrarily low asymptotic density in the natural numbers. We determine the structure of the goups generated by the maps x 7 → x/2 and x 7 → (3x+ 1)/2 modulo b for b
Results 1  10
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