A257210 Numbers n such that the decimal expansions of both n and n^2 have 1 as smallest digit and 7 as largest digit.

271, 371, 1171, 1474, 1475, 1776, 2171, 2271, 2671, 2715, 2761, 3671, 3711, 4174, 4761, 4771, 6761, 7165, 7174, 7261, 7331, 11275, 11474, 11475, 11711, 11715, 11716, 11724, 11725, 11731, 12376, 12715, 12734, 12756, 12776, 13171, 13174, 13275, 13276, 14674

Offset: 1

Author

Felix Fröhlich, Apr 18 2015

Keywords

• nonn
• base

Comments

There are 2 3-digit terms, 19 4-digit terms, 122 5-digit terms, 646 6-digit terms, 3147 7-digit terms, 13300 8-digit terms, 54689 9-digit terms, and 216858 10-digit terms. - Charles R Greathouse IV, Apr 20 2015

Links

• Felix Fröhlich, Table of n, a(n) for n = 1..10000

Crossrefs

Cf. A256630, A256631, A256633, A256634, A256708, A256709, A256889, A257197, A257211.

Programs

Mathematica

fQ[n_] := Block[{d = DigitCount@ n}, Plus @@ Take[d, {8, 10}] == 0 && d[[1]] > 0 && d[[7]] > 0]; Select[Range@ 15000, fQ@ # && fQ[#^2] &] (* Michael De Vlieger, Apr 20 2015 *)

PARI

is(n) = vecmin(digits(n))==1 && vecmin(digits(n^2))==1 && vecmax(digits(n))==7 && vecmax(digits(n^2))==7

PARI

has(n)=my(d=Set(digits(n))); #d && d[1]==1 && d[#d]==7
is(n)=has(n) && has(n^2)
for(d=3,7, for(i=6,7^d-1, v=digits(i,7); if(#v<=d, v=concat(vector(d-#v),v)); if(vecmax(v)==6 && vecmin(v)==0 && has((n=fromdigits(apply(k->k+1,v)))^2), print1(n", ")))) \\ Charles R Greathouse IV, Apr 20 2015