cp's OEIS Frontend

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.

%I A257534 #30 Sep 10 2017 02:20:43
%S A257534 74,74476,74474476
%N 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.
%C A257534 Subsequence of A136948 and of A137139.
%C A257534 a(4) > 10^19, if it exists. - _Giovanni Resta_, May 11 2015
%C A257534 From _Jon E. Schoenfield_, Jun 28 2015: (Start)
%C A257534 a(4) > 6.6666...*10^28, if it exists.
%C A257534 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 A257534 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 A257534 Conjecture: a(4) does not exist. (End)
%C A257534 a(4) > 7.44*10^36, if it exists. - _Chai Wah Wu_, Sep 09 2017
%t A257534 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 A257534 (PARI) is(n) = vecmin(digits(n))==4 && vecmin(digits(n^2))==4 && vecmax(digits(n))==7 && vecmax(digits(n^2))==7
%Y A257534 Cf. A136948, A137139.
%Y A257534 Cf. A256630, A256631, A256633, A256634, A256708, A256709, A256889, A257197, A257210, A257211, A256601, A257310, A249915, A257123, A257368, A257485, A257486, A257498, A238553, A254071, A254072, A254074.
%K A257534 nonn,base,more,bref
%O A257534 1,1
%A A257534 _Felix Fröhlich_, Apr 28 2015