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

1,1

Links

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

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 *)

Prog

(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

Crossrefs

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

Sequence in context: A168352 A147579 A087025 * A161534 A052197 A053076

Adjacent sequences: A249912 A249913 A249914 * A249916 A249917 A249918

Keyword

nonn,base

Author

Felix Fröhlich, Apr 21 2015

Status

approved