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

1,2

Comments

a(24) > 10^30.

Links

Table of n, a(n) for n=1..23.

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 *)

Prog

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

Crossrefs

Cf. A257829, A007954, A004429, A004428.

Sequence in context: A072482 A254958 A302502 * A343050 A276143 A064154

Adjacent sequences: A257827 A257828 A257829 * A257831 A257832 A257833

Keyword

base,nonn

Author

Giovanni Resta, May 10 2015

Status

approved