54954

Appears in sequences

• a(n) = least solution k of f(k) = f(k-1) + ... + f(k-n), where f(m) = prime(m+1)-prime(m) and prime(m) denotes the m-th prime, if k exists; 0 otherwise.at n=8A066496
• Map from binary trees of size n to the set of corresponding trivalent plane trees (tpt) represented as size 2n+1 general trees.at n=29A083930
• p(11p-7) where p is prime.at n=19A098998
• Number of finite, negative, Archimedean, totally ordered monoids of size n (semi-groups with a neutral element that is also the top element).at n=8A253949
• Number of permutations of [n] avoiding the generalized patterns 1(k+2)-(u_1+1)-...-(u_k+1) for all permutations u of [k].at n=63A263791
• Number of rooted tandem duplication trees on n gene segments.at n=9A264868
• Triangular array: For n >= 2 and 0 <= k <= n - 2, T(n, k) equals the number of rooted duplication trees on n gene segments whose leftmost visible duplication event is (k, r), for 1 <= r <= (n - k)/2.at n=52A264869
• Triangular array: For n >= 2 and 0 <= k <= n - 2, T(n, k) equals the number of rooted duplication trees on n gene segments whose leftmost visible duplication event is (k, r), for 1 <= r <= (n - k)/2.at n=53A264869
• Triangular array: For n >= 2 and 0 <= k <= n - 2, T(n, k) equals the number of rooted duplication trees on n gene segments whose leftmost visible duplication event is (k, r), for 1 <= r <= (n - k)/2.at n=54A264869
• G.f. B(x) satisfies: B(x) = 1/((1-x*A(x))*(1-x*C(x)^3)) such that A(x) = 1/((1-x*B(x)^2)*(1-x*C(x)^3)) and C(x) = 1/((1-x*A(x))*(1-x*B(x)^2)) are the g.f.s of A341954 and A341956, respectively.at n=6A341955
• Number of ways to choose 4 disjoint subsets of {1..n} with the same sum and with respectively 1, 2, 3 and 4 distinct elements of {1..n}.at n=29A363517