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

1,1

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

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

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

Crossrefs

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

Sequence in context: A086003 A174402 A048295 * A020363 A051965 A142762

Adjacent sequences: A257207 A257208 A257209 * A257211 A257212 A257213

Keyword

nonn,base

Author

Felix Fröhlich, Apr 18 2015

Status

approved