A181898
Smallest positive integer which cannot be calculated by an expression containing n binary operators (any of add, subtract, multiply and divide) whose operands are any integer between 1 and 9; parentheses allowed.
Original entry on oeis.org
10, 19, 92, 417, 851, 4237, 14771, 73237, 298609
Offset: 0
a(2)=92 because at least 3 operators are required, e.g., (2*7 + 9)*4.
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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
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See Jones link.
A181957
Smallest positive integer which cannot be calculated by an expression containing n binary operators (either add or multiply) whose operands are integers between 1 and 9; parenthesis allowed.
Original entry on oeis.org
10, 19, 92, 239, 829, 2831, 10061, 38231, 189311, 621791, 2853533, 11423579
Offset: 0
a(4) = 239 because at least 4 operators are needed to calculate this value, e.g., (5*5+9)*7+1.
Cf.
A005520 (operand literal is always 1).
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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
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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
A181959
Number of distinct integers that can be generated by an expression containing n binary operators (any of add, subtract, multiply and divide) whose operands are any integer between 1 and 9; parenthesis allowed.
Original entry on oeis.org
9, 48, 236, 1274, 6489, 30229, 142320, 711955, 3601566
Offset: 0
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
A181960
Number of distinct nonnegative integers that can be generated by an expression containing n binary operators (any of add, subtract, multiply and divide) whose operands are any integer between 1 and 9; parenthesis allowed.
Original entry on oeis.org
9, 40, 156, 740, 3668, 16948, 77861, 379084, 1889419
Offset: 0
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
Showing 1-4 of 4 results.