A257830 The decimal representation of the geometric mean of the digits of n starts with the digits of n.

1, 2, 3, 4, 5, 6, 7, 8, 9, 34, 79, 215, 437, 2514, 3833, 32453, 35194, 49672, 5695449, 357129525, 44683966971145538, 383375167535817138, 4377829714163336859592836

Offset: 1

Author

Giovanni Resta, May 10 2015

Keywords

• base
• nonn

Comments

a(24) > 10^30.

Crossrefs

Cf. A257829, A007954, A004429, A004428.

Programs

Mathematica

pr[n_] := Union@Flatten@ Table[Union[ Times @@@ Flatten[Outer[Power, Subsets[ Range@9, {Length@e}], Permutations[e], 1], 1]], {e, IntegerPartitions@ n}]; sol[nd_] := Block[{p = ppr[nd], L}, L = Table[FromDigits[ RealDigits[x^(1/nd), 10, nd][[1]]], {x, p}]; L[[Select[Range@Length@p, Times @@ IntegerDigits[L[[#]]] == p[[#]] &]]]]; Union@ Flatten@ Array[sol, 17] (* terms with up to 17 digits *)

PARI

is(n)=n==sqrtn(prod(i=1,#n=digits(n),n[i]),#n)\10^(1-#n) \\ M. F. Hasler, May 10 2015