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

1,1

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

Links

Table of n, a(n) for n=1..3.

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

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.

Sequence in context: A324523 A145695 A116132 * A063680 A277841 A220472

Adjacent sequences: A257531 A257532 A257533 * A257535 A257536 A257537

Keyword

nonn,base,more,bref

Author

Felix Fröhlich, Apr 28 2015

Status

approved