

A259444


a(1)=2. For n>1, a(n) = smallest number > a(n1) which is different from all the numbers a(i)^a(j) for 1 <= i < n, 1 <= j < n.


3



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

1,1


COMMENTS

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


LINKS

Anders Hellström and Charles R Greathouse IV, Table of n, a(n) for n = 1..10000 (first 1000 terms from Hellström)
Anders Hellström, Sage program
Anders Hellström, Mercury program
Anders Hellström, Ruby program


FORMULA

a(n) = n + sqrt(n) + O(n^(1/3)).  Charles R Greathouse IV, Aug 18 2015


EXAMPLE

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).


PROG

(PARI) first(m)=my(v=vector(m), x, r, n, s); v[1]=2; for(n=2, m, v[n]=v[n1]+1; until(x==1, for(r=1, n1, for(s=1, n1, 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


CROSSREFS

Cf. A007916, A259183 (complement).
Equivalent lexicographically earliest sequences for other operations: A000069 (binary exclusive OR), A005408 (addition), A026424 (multiplication).
Sequence in context: A030159 A030161 A129125 * A071591 A089105 A028769
Adjacent sequences: A259441 A259442 A259443 * A259445 A259446 A259447


KEYWORD

nonn


AUTHOR

Anders Hellström, Jun 27 2015


STATUS

approved



