Sequences

Take list of cubes, move left digit of each term to end of previous term.

Take list of integers n >= 0, move left digit of each term to end of previous term.

Take list of even numbers, move left digit of each term to end of previous term.

Take list of odd numbers, move left digit of each term to end of previous term.

a(n) = floor(n*(n+1)*(n+2) / (n + n+1 + n+2)) = floor(n*(n+2)/3).

Numbers that are congruent to 0 or 1 (mod 3).

a(n) = floor ( n(n+1)(n+2)(n+3) / (n+(n+1)+(n+2)+(n+3)) ).

a(n) = floor( n(n+1)(n+2)(n+3)(n+4) / (n+(n+1)+(n+2)+(n+3)+(n+4)) ).

Numbers that are congruent to {0, 1, 2, 4} mod 5.

Integer quotients of n(n + 1)(n + 2)(n + 3)(n + 4) / (n+(n+1)+(n+2)+(n+3)+(n+4)).

[ n(n+1)(n+2)...(n+5) / (n+(n+1)+(n+2)+...+(n+5)) ].

n(n+1)(n+2)...(n+5) / (n+(n+1)+(n+2)+...+(n+5)) is an integer.

Integer quotients n(n+1)(n+2)...(n+5) / (n+(n+1)+(n+2)+...+(n+5)).

a(n) = floor( n*(n+1)*(n+2)*...*(n+6) / (n+(n+1)+(n+2)+...+(n+6)) ).

Numbers that are congruent to {0, 1, 2, 3, 5, 6} mod 7.

Integer quotients n(n+1)(n+2)...(n+6) / (n+(n+1)+(n+2)+...+(n+6)).

Floor( n(n+1)(n+2)...(n+7) / (n+(n+1)+(n+2)+...+(n+7)) ).

Numbers k such that k*(k+1)*(k+2)*...*(k+7) / (k+(k+1)+(k+2)+...+(k+7)) is an integer.

Integer quotients n(n+1)(n+2)...(n+7) / (n+(n+1)+(n+2)+...+(n+7)).

a(n) = n(n+1)(n+2)...(n+8) / (n+(n+1)+(n+2)+...+(n+8)).

Floor ( n(n+1)(n+2)...(n+9) / (n+(n+1)+(n+2)+...+(n+9)) ).

Numbers k such that k(k+1)(k+2)...(k+9) / (k+(k+1)+(k+2)+...+(k+9)) is an integer.

Integer quotients n(n+1)(n+2)...(n+9) / (n+(n+1)+(n+2)+...+(n+9)).

Numbers k such that k(k+1)(k+2)...(k+11) / (k+(k+1)+(k+2)+...+(k+11)) is an integer.

Numbers k such that k*(k+1)*(k+2) ... (k+13) / (k+(k+1)+(k+2)+ ... +(k+13)) is an integer.

Numbers k such that k(k+1)(k+2)...(k+15) / (k+(k+1)+(k+2)+...+(k+15)) is an integer.

Numbers k such that k(k+1)(k+2)...(k+17) / (k+(k+1)+(k+2)+ ... +(k+17)) is an integer.

Numbers k such that k(k+1)(k+2)...(k+19) / (k+(k+1)+(k+2)+...+(k+19)) is an integer.

Numbers k such that (k*(k+1)*(k+2)) / (k+(k+1)+(k+2)) is a palindrome.

Palindromic quotients (k*(k+1)*(k+2)) / (k+(k+1)+(k+2)).

Numbers k such that k*(k+1)*(k+2) / (k+(k+1)+(k+2)) is a lucky number.

Quotients k*(k+1)*(k+2) / (k+(k+1)+(k+2)) that are lucky numbers.

Numbers that are congruent to {1, 2, 4} mod 5.

Positive integers of the form n(n+1)(n+2)(n+3)(n+4)/(n+(n+1)+(n+2)+(n+3)+(n+4)) that are a multiple of n.

Positive numbers k such that (k+1)*(k+2)*(k+3)*(k+4)/(k+(k+1)+(k+2)+(k+3)+(k+4)) is an integer.

Numbers that are congruent to {1, 2, 3, 5, 6} mod 7.

Numbers n such that n(n+1)(n+2)...(n+10) /(n+(n+1)+(n+2)+...+(n+10)) is a multiple of n.

Numbers such that n(n+1)(n+2)...(n+12) / (n+(n+1)+(n+2)+...+(n+12)) is a multiple of n.

Numbers k such that k equals the sum of its digits raised to the consecutive powers (1,2,3,...).

If there were a 9-dimensional unimodular lattice with minimal norm 2, this would be its theta series; however, no such lattice exists.

Number of unordered sets a, b, c, d of distinct integers from 1..n such that a+b+c+d = 0 (mod n).

Theta series of extremal odd unimodular lattice D_8^{+2} with minimal norm 2 in dimension 16.

Expansion of Sum_{i>=0} q^i*theta_3^i.

Numbers whose set of base-4 digits is {2,3}.

Numbers whose set of base-5 digits is {2,3}.

Numbers whose set of base-6 digits is {2,3}.

Numbers whose set of base-7 digits is {2,3}.

Numbers whose set of base-8 digits is {2,3}.

Numbers whose set of base-9 digits is {2,3}.

Numbers using only digits 2 and 3.