A249915 Numbers k such that the decimal expansions of both k and k^2 have 2 as smallest digit and 6 as largest digit.

255465, 652244, 665256, 2534665, 2536656, 2554262, 6523462, 6524235, 6652242, 23352656, 23354365, 23523462, 23546665, 23565325, 25346665, 25425256, 25624665, 25625465, 65226242, 65234535, 235442656, 254234662, 255465525, 255645525, 256246665, 256254665

Offset: 1

Author

Felix Fröhlich, Apr 21 2015

Keywords

• nonn
• base

Links

• Chai Wah Wu, Table of n, a(n) for n = 1..2000 (n = 1..42 from Robert Israel).

Crossrefs

Cf. A137067, A137079, A137093, A256630, A256631, A256633, A256634, A256708, A256709, A256889, A257197, A257210, A257211, A256601, A257310.

Programs

Maple

M:= 10:
B:= [[2],[3],[4],[5],[6]]:
A:= NULL:
for d from 2 to M do
  B:= map(b -> seq([op(b), i],i=2..6), B);
  C:= select(b -> max(b)=6 and min(b) = 2, B);
  X:= map(b -> add(b[i]*10^(d-i),i=1..d),C);
  X:= select(proc(x) local L; L:= convert(x^2,base,10); max(L) = 6 and min(L) = 2 end proc, X);
  A:= A, op(X);
od:
A; # Robert Israel, Apr 27 2015

Mathematica

fQ[n_] := Block[{d = DigitCount@ n}, Plus @@ Prepend[Take[d, -4], First@ d] == 0 && d[[2]] > 0 && d[[6]] > 0]; Select[Range@ 2600000, fQ@ # && fQ[#^2] &] (* Michael De Vlieger, Apr 27 2015 *)

PARI

is(n) = vecmin(digits(n))==2 && vecmin(digits(n^2))==2 && vecmax(digits(n))==6 && vecmax(digits(n^2))==6

Python

from itertools import product
A249915_list = []
for l in range(10):
    for a in product('23456', repeat = l):
        for b in ('2', '4', '5', '6'):
            s = ''.join(a)+b
            if '2' in s and '6' in s:
                n = int(s)
                if {'2', '6'} <= set(str(n**2)) <= {'2', '3', '4', '5', '6'}:
                    A249915_list.append(n) # Chai Wah Wu, Apr 29 2015