A034060 a(n) is the least k (not a 5th power) such that the decimal part of k^(1/5) starts with n.

33, 2, 3, 4, 6, 8, 11, 15, 19, 25, 41, 42, 43, 44, 2, 46, 48, 49, 50, 51, 52, 53, 54, 56, 3, 58, 59, 61, 62, 63, 65, 4, 68, 69, 71, 72, 74, 5, 77, 78, 80, 82, 83, 6, 87, 89, 91, 7, 94, 96, 98, 8, 102, 104, 106, 9, 110, 113, 10, 117, 119, 11

Offset

0,1

Links

Robert Israel, Table of n, a(n) for n = 0..9999

Example

a(0)=33 because 33^(1/5) = 2.0123466... and 0123466... starts with 0, and there is no k < 33 whose 5th root has this property.
a(1)=2 because 2^(1/5) = 1.1486983... and 1486983... starts with 1, and there is no k < 2 whose 5th root has this property.

Maple

d:= 2: # for a(0) .. a(10^d-1)
V:= Array(0..10^d-1): V[0]:= 33: count:= 1:
for x from 2 while count < 10^d do
  v:= floor(10^d*x^(1/5)) mod 10^d;
if v < 10^(d-1) then next fi;
  for i from 1 to d do
    w:= floor(v/10^(d-i));
    if V[w] = 0 then V[w]:= x; count:= count+1; fi
  od
od:
convert(V, list); # Robert Israel, Jun 20 2023

Crossrefs

Cf. A034070, A034080.

Sequence in context: A279364 A308408 A263169 * A032445 A333128 A135088

Adjacent sequences: A034057 A034058 A034059 * A034061 A034062 A034063

Keyword

nonn,base

Author

Patrick De Geest, Sep 15 1998

Extensions

Edited by Robert Israel, Jun 21 2023

Status

approved