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A264733
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a(n) is the smallest number > 1 such that the concatenation a(1)a(2)...a(n) is a perfect power.
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6
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4, 9, 13, 31556, 4433200001, 7330164793357114944, 364233003001227343654904892703798707409, 30558883460500823396683989630832748682356643682219859233661160618544138815441
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OFFSET
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1,1
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LINKS
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MAPLE
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a[1]:= 4: C:= 4:
for n from 2 to 9 do
looking:= true;
for d from 1 while looking do
L:= 10^d*C + 10^(d-1);
U:= 10^d*C + 10^d - 1;
p:= 1;
while p < ilog2(U) do
p:= nextprime(p);
Lp:= ceil(L^(1/p));
Up:= floor(U^(1/p));
while not (Lp::integer and Up::integer) do
Digits:= 2*Digits;
Lp:= eval(Lp);
Up:= eval(Up);
od;
if Lp <= Up then
Cp:= Lp^p;
a[n]:= Cp - 10^d*C;
C:= Cp;
looking:= false;
break
fi
od
od
od:
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MATHEMATICA
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a = {}; Do[k = 2; While[! Or[# == 1, GCD @@ FactorInteger[#][[All, -1]] > 1] &@ FromDigits@ Flatten@ Join[#, IntegerDigits@ k], k++] &@ Map[IntegerDigits, a]; AppendTo[a, k], {i, 4}]; a (* Michael De Vlieger, Jan 23 2017 *)
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PROG
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(PARI) first(m)=my(s="4"); print1(4, ", "); for(i=2, m, n=1; while(!ispower(eval(concat(s, Str(n)))), n++); print1(n, ", "); s=concat(s, Str(n)))
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CROSSREFS
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Cf. A001597(perfect powers), A051671, A061109, A061110, A261696, A264738, A264776, A264777, A264804, A264842, A264848, A264849.
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KEYWORD
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nonn,base,hard
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AUTHOR
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EXTENSIONS
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STATUS
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approved
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