All Questions
Tagged with integer-sequences reference-request
9 questions with no upvoted or accepted answers
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Elliptic curve sequences needed for universal forgery
Elliptic Curve Digital Signature Algorithm (ECDSA) admits universal forgery (UF) if the Attacker can solve the equation
$$z=\frac{f_{k-1}(x,y)f_{k+1}(x,y)}{f_{k}(x,y)^2},$$
where $k$ is unknown, $f_{k}...
- 12.3k
3
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Is there a name for this operation on integer functions?
Suppose $f$ and $g$ are functions from $\mathbb N^+$ to itself. I want to consider the function $f^g$, where $f^g(n) = f \circ \dots \circ f(n)$, where composition is done $g(n)$-many times. Note ...
- 18.7k
3
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Permutation of a sequence, such that $y_i+y_{i+1}$ are all distinct
The sequence $x_1, x_2, ..., x_n$ of positive integers contains at least $\frac {2n}{3}+1$ distinct numbers and each of them appears at most three times. How to prove that there is a permutation $y_1, ...
- 3,153
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Does the divergent solution of this equation :$f'=e^{f^{-1}}$ of Gevrey type and could be Borel summation applied for it?
This question was asked here in MO by someone seeking for the solution of the functional -differential:$f'=e^{f^{-1}}$ not exactly an O.D.E, and again here seeking for the growth rate of it solution ...
user99666
2
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Equi-distribution of the parity of partitions
The integer partition function $p(n)$ has a generating function given by
$$\frac1{(q)_{\infty}}=\sum_{n=0}^{\infty}p(n)q^n$$
with $(q)_{\infty}=\prod_{m=1}^{\infty}(1-q^m)$. The long-standing problem ...
- 43.2k
1
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Raggedness measure of a sequence
This surely has been done, maybe I googled the wrong adjective...
Define a raggedness measure $r$ of a sequence $S$ in this way:
Two members $S_i,S_j$ of the sequence (who don't have to be adjacent!) ...
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Question related to sequence of recurrence relation $a_k=\operatorname{rad}(a_{k-1}+a_{k-2})$ for $k\ge 2$ where $a_0=0,a_1=1$
Define radical of an integer Wiki
$$\displaystyle{\mathrm{rad}}(n)=\prod_{{\scriptstyle p\mid n\atop p\:{\text{prime}}}}p$$
Example $n=504=2^3\cdot3^2\cdot7$ therefore ${\displaystyle \operatorname{...
- 599
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Reference request: Counting integer sequences in homogeneous linear recurrences
Are there references in the literature that deal with the probability of finding an integer sequence in a linear homogeneous recurrence with constant coefficients $ \in \mathbb{Z}$? (or provides a way ...
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Polynomials of integer coefficients that evaluated at Mersenne or Fermat numbers produce square-free integers
Mersenne numbers $M_n=2^n-1$ and Fermat numbers $F_n=2^{2^n}+1$ draw the attention of professional mathematicians to get prime constellations or statements related to primality tests for these ...
