OFFSET
1,1
COMMENTS
a(4) > 10^19, if it exists. - Giovanni Resta, May 11 2015
From Jon E. Schoenfield, Jun 28 2015: (Start)
a(4) > 6.6666...*10^28, if it exists.
Define a property P1 such that, for any positive integer k, P1(k) is true iff the smallest- and largest-valued digits of the decimal expansion of k are 4 and 7, respectively. This sequence lists the positive integers n such that both P1(n) and P1(n^2) are true.
Define a less-restrictive property P2 such that, for any positive integer k, P2(k) is true iff the smallest- and largest-valued digits of the decimal expansion of k are at least 4 and at most 7, respectively. There exist only four positive integers n < 6.6666...*10^28, such that both P2(n) and P2(n^2) are true: a(1), a(2), a(3), and 76 (whose square, 5776, has minimum digit 5).
Conjecture: a(4) does not exist. (End)
a(4) > 7.44*10^36, if it exists. - Chai Wah Wu, Sep 09 2017
MATHEMATICA
fQ[n_] := Block[{c = DigitCount@ n}, And[Plus @@ Take[c, {1, 3}] == 0, Plus @@ Take[c, {8, 10}] == 0, c[[4]] > 0, c[[7]] > 0]]; Select[Range@ 1000000, fQ@ # && fQ[#^2] &] (* Michael De Vlieger, May 05 2015 *)
PROG
(PARI) is(n) = vecmin(digits(n))==4 && vecmin(digits(n^2))==4 && vecmax(digits(n))==7 && vecmax(digits(n^2))==7
CROSSREFS
KEYWORD
nonn,base,more,bref
AUTHOR
Felix Fröhlich, Apr 28 2015
STATUS
approved