A257534 Numbers n such that the decimal expansions of both n and n^2 have 4 as the digit with the smallest value and 7 as the digit with the largest value.

74, 74476, 74474476

Offset: 1

Author

Felix Fröhlich, Apr 28 2015

Keywords

• nonn
• base
• more
• bref

Comments

Subsequence of A136948 and of A137139.

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

Crossrefs

Cf. A136948, A137139.

Cf. A256630, A256631, A256633, A256634, A256708, A256709, A256889, A257197, A257210, A257211, A256601, A257310, A249915, A257123, A257368, A257485, A257486, A257498, A238553, A254071, A254072, A254074.

Programs

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 *)

PARI

is(n) = vecmin(digits(n))==4 && vecmin(digits(n^2))==4 && vecmax(digits(n))==7 && vecmax(digits(n^2))==7