A257534 - OEIS

%I #30 Sep 10 2017 02:20:43

%S 74,74476,74474476

%N 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.

%C Subsequence of A136948 and of A137139.

%C a(4) > 10^19, if it exists. - _Giovanni Resta_, May 11 2015

%C From _Jon E. Schoenfield_, Jun 28 2015: (Start)

%C a(4) > 6.6666...*10^28, if it exists.

%C 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.

%C 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).

%C Conjecture: a(4) does not exist. (End)

%C a(4) > 7.44*10^36, if it exists. - _Chai Wah Wu_, Sep 09 2017

%t 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 *)

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

%Y Cf. A136948, A137139.

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

%K nonn,base,more,bref

%O 1,1

%A _Felix Fröhlich_, Apr 28 2015