A264733 a(n) is the smallest number > 1 such that the concatenation a(1)a(2)...a(n) is a perfect power.

4, 9, 13, 31556, 4433200001, 7330164793357114944, 364233003001227343654904892703798707409, 30558883460500823396683989630832748682356643682219859233661160618544138815441

Offset: 1

Author

Anders Hellström, Nov 22 2015

Keywords

• nonn
• base
• hard

Links

• Robert Israel, Table of n, a(n) for n = 1..10
• Amarnath Murthy, Exploring some new ideas on Smarandache type sets, functions and sequences, Smarandache Notions Journal Vol. 11 N. 1-2-3 Spring 2000. p. 172 (breakup sequences).

Crossrefs

Cf. A001597(perfect powers), A051671, A061109, A061110, A261696, A264738, A264776, A264777, A264804, A264842, A264848, A264849.

Programs

Maple

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:
seq(a[i],i=1..9); # Robert Israel, Nov 27 2015

Mathematica

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 *)

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)))

Extensions

a(5)-a(8) from Jon E. Schoenfield, Nov 22 2015