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# User:Doug Bell

From OeisWiki

Software architect and recreational mathematician. Create original mathematical and logic puzzles (for some examples see my contributions on Braingle). Primary author of the Wikipedia pages on poker probability.

In my distant past I was the lead developer on the internationally award winning hall-of-fame computer game *Dungeon Master*.

## OEIS Contributions

### Sequences added

- A153745 - Numbers n such that the number of digits d in n^2 is not prime and for each factor f of d the sum of the d/f digit groupings in n^2 of size f is a square.
- A153746 - Numbers n such that there are 8 digits in n^2 and for each factor f of 8 (1,2,4) the sum of digit groupings of size f is a square.
- A153747 - Numbers n such that there are 9 digits in n^2 and for each factor f of 9 (1,3) the sum of digit groupings of size f is a square.
- A153748 - Numbers n such that there are 10 digits in n^2 and for each factor f of 10 (1, 2, 5) the sum of digit groupings of size f is a square.
- A153749 - Numbers n such that there are 12 digits in n^2 and for each factor f of 12 (1,2,3,4,6) the sum of digit groupings of size f is a square.
- A153750 - Numbers n such that there are 14 digits in n^2 and for each factor f of 14 (1,2,7) the sum of digit groupings of size f is a square.
- A153751 - Numbers n such that there are 15 digits in n^2 and for each factor f of 15 (1,3,5) the sum of digit groupings of size f is a square.
- A153752 - Numbers n such that there are 16 digits in n^2 and for each factor f of 16 (1,2,4,8) the sum of digit groupings of size f is a square.
- A153753 - Numbers n such that there are 18 digits in n^2 and for each factor f of 18 (1,2,3,6,9) the sum of digit groupings of size f is a square.
- A258660 - Numbers n such that the number of digits d in n is not prime and for each factor f of d the sum of the d/f digit groupings of size f is a square.
- A258663 - Numbers n such that 9n-1 is prime.
- A259194 - Number of partitions of n into four primes.
- A259195 - Number of partitions of n into five primes.
- A259196 - Number of partitions of n into six primes.
- A259197 - Number of partitions of n into seven primes.
- A259198 - Number of partitions of n into eight primes.
- A259200 - Number of partitions of n into nine primes.
- A259201 - Number of partitions of n into ten primes.
- A259254 - Number of partitions of prime(n) into n primes.
- A259299 - The decimal expansion of n/(n+1) until it terminates or repeats, shown without the decimal point.
- A259362 - a(1) = 1, for n > 1: a(n) is the number of ways to write n as a nontrivial perfect power.
- A285936 - Number of rotations of the digits in n produced by n * x/y where x != y.
- A287618 - Triangle read by rows: T(j,k) is the number of distinct edge segments in a j X k rectangular grid.
- A287688 - Triangle read by rows: T(j,k) is the number of distinct edge segment pairs in a j X k rectangular grid.
- A288626 - Numbers n such that n * (x-1)/x produces a rotation of the digits in n for some value of x.
- A288669 - Numbers n such that n * x/(x-1) produces a rotation of the digits in n for some value of x.

### Sequences contributed to

*Not included below are several sequences where I added keywords or corrected formatting.*

- A000040 - The prime numbers.
- A000071 - Fibonacci numbers - 1.
- A000295 - Eulerian numbers.
- A000302 - Powers of 4.
- A000332 - Binomial coefficient binomial(n,4) = n*(n-1)*(n-2)*(n-3)/24.
- A000351 - Powers of 5.
- A000466 - 4*n^2 - 1.
- A001511 - The ruler function: 2^a(n) divides 2n. Or, a(n) = 2-adic valuation of 2n.
- A001844 - Centered square numbers: 2n(n+1)+1. Sums of two consecutive squares.
- A005899 - Number of points on surface of octahedron: a(0) = 1; for n>0, ( or ) a(n) = 4n^2 + 2, coordination sequence for cubic lattice.
- A006519 - Highest power of 2 dividing n.
- A008456 - 12th powers: a(n) = n^12.
- A008532 - Coordination sequence for 4-dimensional I-centered cubic orthogonal lattice.
- A008959 - Final digit of squares: n^2 mod 10.
- A008960 - Final digit of cubes: n^3 mod 10.
- A010879 - Final digit of n.
- A038154 - a(n) = n! * Sum_{k=0..n-2} 1/k!.
- A040040 - Average of twin prime pairs (A014574), divided by 2.
- A045572 - Numbers that are odd but not divisible by 5.
- A056220 - a(n) = 2*n^2-1.
- A059722 - a(n) = n*(2*n^2 - 2*n + 1).
- A061242 - Primes of the form 9n - 1.
- A069074 - (2*n+2)*(2*n+3)*(2*n+4) = 24*A000330(n+1).
- A070514 - Final digit of n^4: n^4 mod 10.
- A079309 - a(n) = C(1,1)+C(3,2)+C(5,3)+...+C(2n-1,n).
- A089361 - Numbers of pairs (i, j), i, j > 1, such that i^j <= n.
- A143954 - Number of peaks in the peak plateaux of all Dyck paths of semilength n.
- A235589 - The periodic part of the decimal expansion of m/(m+1), for those m/(m+1) that have pure periods.
- A251728 - Semiprimes p*q for which p <= q < p^2.