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A259444
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a(1)=2. For n>1, a(n) = smallest number > a(n-1) which is different from all the numbers a(i)^a(j) for 1 <= i < n, 1 <= j < n.
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3
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2, 3, 5, 6, 7, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21, 22, 23, 24, 26, 28, 29, 30, 31, 33, 34, 35, 37, 38, 39, 40, 41, 42, 43, 44, 45, 46, 47, 48, 50, 51, 52, 53, 54, 55, 56, 57, 58, 59, 60, 61, 62, 63, 65, 66, 67, 68, 69, 70, 71, 72, 73, 74, 75, 76
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OFFSET
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1,1
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COMMENTS
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Lexicographically earliest sequence of distinct nonnegative integers with no term being the result of any term raised to the power of any term. - Peter Munn, Mar 15 2018
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LINKS
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FORMULA
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EXAMPLE
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After 2, we have to avoid 2^2 = 4, so 3 works.
After 2,3 we have to avoid 2^2=4, 2^3=8, 3^2=9, 3^3=27, so 5 works,also 6, also 7. Then 10, 11 and so on.
Note that 16 is the term after 15, because 2^4 and 4^2 are not excluded (since 4 is not in the sequence).
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PROG
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(PARI) first(m)=my(v=vector(m), x, r, n, s); v[1]=2; for(n=2, m, v[n]=v[n-1]+1; until(x==1, for(r=1, n-1, for(s=1, n-1, if((v[r]^v[s])===v[n]||(v[s]^v[r])===v[n], v[n]++; x=0; break(2), x=1))))); v;
(PARI) list(lim)=if(lim<5, return(if(lim<3, if(lim<2, [], [2]), [2, 3]))); my(u=list(max(sqrtint(lim\=1), 3)), v=vectorsmall(lim\=1, i, 1), r, m, t); for(i=2, #u, v[i]=!!setsearch(u, i)); for(r=1, #u, if(2^u[r]>lim, break); m=0; while(m++<=#u && (t=u[m]^u[r])<=lim, v[t]=0)); u=List(); for(i=2, #v, if(v[i], listput(u, i))); Vec(u) \\ Charles R Greathouse IV, Aug 18 2015
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CROSSREFS
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Equivalent lexicographically earliest sequences for other operations: A000069 (binary exclusive OR), A005408 (addition), A026424 (multiplication).
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KEYWORD
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nonn
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AUTHOR
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STATUS
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approved
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