A083807 Perfect powers using only composite digits 4,6,8,9 and 0.

4, 8, 9, 49, 64, 400, 484, 900, 4096, 4489, 4900, 6084, 6400, 6889, 8000, 8464, 8649, 9409, 9604, 40000, 40804, 44944, 48400, 64000, 64009, 66049, 68644, 69696, 80089, 88804, 90000, 94864, 400689, 404496, 409600, 440896, 444889, 448900, 466489

Offset

1,1

Comments

Call terms trivial if they are of the form 10^k*a(m) (e.g., 400,40000,900,90000). Conjecture: sequence has infinitely many nontrivial terms.

Links

Charles R Greathouse IV, Table of n, a(n) for n = 1..10000

Mathematica

ppQ[n_]:=GCD@@FactorInteger[n][[All, 2]]>1; Select[FromDigits/@ Tuples[{0, 4, 6, 8, 9}, 6], ppQ] (* Harvey P. Dale, Aug 12 2020 *)

Prog

(PARI) list(lim)=my(v=List(), u=[0, 4, 6, 8, 9]); forprime(e=2, log(lim+=.5)\log(2), for(b=2, lim^(1/e), if(vecsort(concat(digits(b^e), u), , 8)==u, listput(v, b^e)))); vecsort(Vec(v), , 8) \\ Charles R Greathouse IV, Mar 20 2013

Crossrefs

Cf. A083806.

Sequence in context: A035132 A077572 A239520 * A098128 A217700 A118895

Adjacent sequences: A083804 A083805 A083806 * A083808 A083809 A083810

Keyword

base,nonn

Author

Amarnath Murthy and Meenakshi Srikanth (menakan_s(AT)yahoo.com), May 08 2003

Extensions

More terms from Matthew Ohlsen (mjo178(AT)psu.edu), Feb 26 2006

Missing terms added by Charles R Greathouse IV, Mar 20 2013

Status

approved