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A257210
Numbers n such that the decimal expansions of both n and n^2 have 1 as smallest digit and 7 as largest digit.
16
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
1,1
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
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 *)
PROG
(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
KEYWORD
nonn,base
AUTHOR
Felix Fröhlich, Apr 18 2015
STATUS
approved