This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.
Derek M. Jones has authored 5 sequences.
a(1)=40, the distinct values are: 0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 20 21 24 25 27 28 30 32 35 36 40 42 45 48 49 54 56 63 64 72 81
a(1)=48, the distinct values are -8 -7 -6 -5 -4 -3 -2 -1 0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 20 21 24 25 27 28 30 32 35 36 40 42 45 48 49 54 56 63 64 72 81
a(1) = 93 and the distinct values are -8, -7, -6, -5, -4, -3, -2, -1, 1/9, 1/8, 1/7, 1/6, 1/5, 2/9, 1/4, 2/7, 1/3, 3/8, 2/5, 3/7, 4/9, 1/2, 5/9, 4/7, 3/5, 5/8, 2/3, 5/7, 3/4, 7/9, 4/5, 5/6, 6/7, 7/8, 8/9, 1, 9/8, 8/7, 7/6, 6/5, 5/4, 9/7, 4/3, 7/5, 3/2, 8/5, 5/3, 7/4, 9/5, 2, 9/4, 7/3, 5/2, 8/3, 3, 7/2, 4, 9/2, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 20, 21, 24, 25, 27, 28, 30, 32, 35, 36, 40, 42, 45, 48, 49, 54, 56, 63, 64, 72, 81
a(4) = 239 because at least 4 operators are needed to calculate this value, e.g., (5*5+9)*7+1.
first(n)=my(op=[(x, y)->x+y, (x, y)->x*y], v=vector(n+1), t); v[1]=[1..9]; for(k=2, #v, my(u=[]); for(i=1, (k+1)\2, my(a=v[i], b=v[k-i]); t=Set(concat(apply(f->setbinop(f, a, b), op))); u=concat(u, t)); v[k]=setminus(Set(u), [0])); t=10; for(i=1, #v, while(setsearch(v[i], t), t++); v[i]=t); v; print(first(7)) \\ Michael S. Branicky, Oct 19 2021 after Charles R Greathouse IV in A181898
def aupton(nn):
alst = [10]
R = {0: set(range(1, 10))} # R[n] is set reachable using n ops
for n in range(1, nn):
R[n] = set()
for i in range((n+1)//2):
for a in R[i]:
for b in R[n-1-i]:
R[n].update([a+b, a*b])
k = 10
while k in R[n]: k += 1 # n.b. R[n-1] <= R[n] due to * by 1
alst.append(k)
return alst
print(aupton(9)) # Michael S. Branicky, Oct 19 2021
a(2)=92 because at least 3 operators are required, e.g., (2*7 + 9)*4.
first(n)=my(op=[(x,y)->x+y, (x,y)->x-y, (x,y)->y-x, (x,y)->x*y, (x,y)->x/y, (x,y)->y/x], v=vector(n+1), t); v[1]=[1..9]; for(k=2,#v, my(u=[]); for(i=1,(k+1)\2, my(a=v[i],b=v[k-i]); t=Set(concat(apply(f->setbinop(f,a,b), op))); u=concat(u,t)); v[k]=setminus(Set(u), [0])); t=10; for(i=1,#v, while(setsearch(v[i],t), t++); v[i]=t); v \\ Charles R Greathouse IV, Jan 09 2017
See Jones link.