A256708 -id:A256708 - cp's OEIS frontend

A256631 Numbers n such that the decimal expansions of both n and n^2 have 0 as smallest digit and 5 as largest digit.

50, 105, 150, 205, 350, 450, 500, 501, 502, 505, 550, 1005, 1015, 1050, 1055, 1105, 1150, 1205, 1450, 1500, 1501, 1550, 2005, 2050, 2055, 2105, 2305, 2350, 3350, 3500, 4500, 5000, 5001, 5002, 5005, 5010, 5011, 5012, 5015, 5020, 5021, 5032, 5045, 5050, 5055

Offset: 1

Felix Fröhlich, Apr 05 2015

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

Cf. A136817, A256630, A256633, A256634, A256708, A256709, A256889, A257086.

fQ[n_] := Block[{c = DigitCount@ n}, And[Plus @@ Take[c, {6, 9}] == 0, c[[5]] > 0, c[[10]] > 0]]; Select[Range@ 5100, fQ@ # && fQ[#^2] &] (* Michael De Vlieger, Apr 12 2015 *)
Select[Range[5100],Min[IntegerDigits[#]]==0&&Max[IntegerDigits[#] ]== 5 && Min[IntegerDigits[#^2]]==0&&Max[IntegerDigits[#^2]]==5&] (* Harvey P. Dale, Jan 19 2020 *)

is(n) = vecmin(digits(n))==0 && vecmin(digits(n^2))==0 && vecmax(digits(n))==5 && vecmax(digits(n^2))==5

A256633 Numbers n such that the decimal expansions of both n and n^2 have 0 as smallest digit and 6 as largest digit.

Original entry on oeis.org

60, 160, 460, 506, 560, 600, 601, 602, 605, 660, 1006, 1016, 1060, 1160, 1460, 1560, 1600, 1601, 1602, 1620, 2006, 2016, 2060, 2160, 2460, 2560, 3606, 4506, 4600, 4605, 4650, 5006, 5016, 5060, 5160, 5506, 5600, 5605, 5660, 6000, 6001, 6002, 6005, 6010, 6020

Offset: 1

Felix Fröhlich, Apr 05 2015

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

Cf. A256630, A256631, A256634, A256708, A256709, A256889, A257085.

fQ[n_] := Block[{c = DigitCount@ n}, And[Plus @@ Take[c, {7, 9}] == 0, c[[6]] > 0, c[[10]] > 0]]; Select[Range@ 6400, fQ@ # && fQ[#^2] &] (* Michael De Vlieger, Apr 12 2015 *)
Select[Range[6100],With[{idn=IntegerDigits[#],idn2=IntegerDigits[#^2]},Min[idn]==Min[idn2]==0&&Max[idn]==Max[idn2]==6]&] (* Harvey P. Dale, Feb 06 2025 *)

is(n) = vecmin(digits(n))==0 && vecmin(digits(n^2))==0 && vecmax(digits(n))==6 && vecmax(digits(n^2))==6

A256630 Numbers n such that the decimal expansions of both n and n^2 have 0 as smallest digit and 4 as largest digit.

Original entry on oeis.org

142201, 1422010, 11141110, 11411110, 11412021, 14220100, 20323421, 21024111, 101203421, 110141011, 110142201, 111411100, 114111100, 114120210, 120013421, 141433102, 142201000, 203234210, 210241110, 1012034210, 1101410011, 1101410110, 1101422010, 1114111000

Offset: 1

Felix Fröhlich, Apr 05 2015

Chai Wah Wu, Table of n, a(n) for n = 1..10000

Cf. A256631, A256633, A256634, A256708, A256709, A256889.

Subsequence of A136810.

fQ[n_] := Block[{c = DigitCount@ n}, And[Plus @@ Take[c, {5, 9}] == 0, c[[4]] > 0, c[[10]] > 0]]; Select[Range@ 10000000, fQ@ # && fQ[#^2] &] (* Michael De Vlieger, Apr 12 2015 *)

is(n) = vecmin(digits(n))==0 && vecmin(digits(n^2))==0 && vecmax(digits(n))==4 && vecmax(digits(n^2))==4

from itertools import product
A256630_list = []
for l in range(11):
    for a in ('1','2','3','4'):
        for b in product('01234',repeat = l):
            for c in ('0','1','2'):
                s = a+''.join(b)+c
                if '0' in s and '4' in s:
                    n = int(s)
                    s2 = set(str(n**2))
                    if {'0','4'} <= s2 <= {'0','1','2','3','4'}:
                        A256630_list.append(n)
print(A256630_list) # Chai Wah Wu, Apr 17 2015

More terms from Alois P. Heinz, Apr 16 2015

A256634 Numbers n such that the decimal expansions of both n and n^2 have 0 as smallest digit and 7 as largest digit.

Original entry on oeis.org

740, 760, 1071, 1740, 2074, 2705, 2710, 2740, 2750, 2760, 3705, 3710, 3760, 4071, 4705, 4740, 4760, 5071, 5705, 5760, 6740, 7074, 7240, 7260, 7400, 7550, 7560, 7600, 7601, 7760, 10076, 10174, 10274, 10275, 10371, 10375, 10376, 10571, 10710, 10724, 10726, 10740

Offset: 1

Felix Fröhlich, Apr 05 2015

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

Cf. A136813, A256630, A256631, A256633, A256708, A256709.

fQ[n_] := Block[{c = DigitCount@ n}, And[Plus @@ Take[c, {8, 9}] == 0, c[[7]] > 0, c[[10]] > 0]]; Select[Range@ 10800, fQ@ # && fQ[#^2] &] (* Michael De Vlieger, Apr 12 2015 *)

is(n) = vecmin(digits(n))==0 && vecmin(digits(n^2))==0 && vecmax(digits(n))==7 && vecmax(digits(n^2))==7

A256709 Numbers n such that the decimal expansions of both n and n^2 have 0 as smallest digit and 9 as largest digit.

Original entry on oeis.org

509, 890, 903, 905, 930, 950, 960, 970, 980, 990, 1039, 1091, 1095, 1097, 1390, 1709, 1903, 1905, 1930, 1970, 1980, 1990, 2049, 2093, 2095, 2097, 2190, 2509, 2809, 2903, 2905, 2907, 2930, 2970, 2990, 3009, 3049, 3079, 3090, 3092, 3095, 3097, 3098, 3099, 3209

Offset: 1

Felix Fröhlich, Apr 08 2015

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

Cf. A136836, A256630, A256631, A256633, A256634, A256708.

fQ[n_] := Block[{c = DigitCount@ n}, And[c[[9]] > 0, c[[10]] > 0]]; Select[Range@ 3209, fQ@ # && fQ[#^2] &] (* Michael De Vlieger, Apr 12 2015 *)

is(n) = vecmin(digits(n))==0 && vecmin(digits(n^2))==0 && vecmax(digits(n))==9 && vecmax(digits(n^2))==9

A256889 Numbers k such that the decimal expansions of both k and k^2 have 1 as smallest digit and 5 as largest digit.

Original entry on oeis.org

115, 1115, 1235, 3515, 11115, 12335, 12415, 33515, 35415, 123335, 123512, 124235, 145415, 152132, 231115, 235211, 333515, 1114115, 1155211, 1233335, 1531115, 1534312, 2311115, 3333515, 11114115, 11141115, 11145511, 12333335, 12342335, 15334312, 15531115

Offset: 1

Felix Fröhlich, Apr 12 2015

k can only begin with 1, 2 or 3 and k mod 10 can only equal 1, 2 or 5. - Robert G. Wilson v, Apr 13 2015

Heuristics suggest that this sequence should be infinite and the sequence with 4 in place of 5 should be finite. The latter sequence contains no terms up to 10^30. - Charles R Greathouse IV, Mar 20 2022

Chai Wah Wu, Table of n, a(n) for n = 1..2000 (n = 1..75 from Robert G. Wilson v).

Cf. A256630, A256631, A256633, A256634, A256708, A256709.

fQ[n_] := Block[{c = DigitCount@ n}, And[Plus @@ Take[c, {6, 10}] == 0, c[[1]] > 0, c[[5]] > 0]]; Select[Range@ 100000, fQ@ # && fQ[#^2] &] (* Michael De Vlieger, Apr 12 2015 *)
fQ[n_] := Block[{id1 = Union@ IntegerDigits[ n], id2 = Union@ IntegerDigits[ n^2]}, Min[id1] == Min[id2] == 1 && Max[id1] == Max[id2] == 5]; k = 1; lst = {}; While[k < 10^7, If[ fQ@ k, AppendTo[lst, k]]; k++; If[ fQ@ k, AppendTo[lst, k]]; k += 3; If[ fQ@ k, AppendTo[lst, k]]; k += 6]; lst (* Robert G. Wilson v, Apr 13 2015 *)

is(n) = vecmin(digits(n))==1 && vecmin(digits(n^2))==1 && vecmax(digits(n))==5 && vecmax(digits(n^2))==5

A257197 Numbers k such that the decimal expansions of both k and k^2 have 1 as smallest digit and 6 as largest digit.

Original entry on oeis.org

116, 146, 1116, 1146, 1156, 1246, 1465, 1556, 1616, 3516, 3621, 4611, 4621, 4631, 11116, 11146, 11156, 11465, 11556, 11642, 15216, 16231, 21556, 22631, 25146, 25162, 25621, 33516, 34156, 35116, 35146, 35162, 36211, 36215, 36512, 46111, 46112, 46211, 46331

Offset: 1

Felix Fröhlich, Apr 18 2015

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

Cf. A256630, A256631, A256633, A256634, A256708, A256709, A256889, A257210, A257211.

sd1Q[n_]:=Module[{idn=IntegerDigits[n]},Min[idn]==1&&Max[idn]==6]; Select[ Range[50000],AllTrue[{#,#^2},sd1Q]&] (* Requires Mathematica version 10 or later *) (* Harvey P. Dale, Nov 22 2020 *)

is(n) = vecmin(digits(n))==1 && vecmin(digits(n^2))==1 && vecmax(digits(n))==6 && vecmax(digits(n^2))==6

Corrected b-file from Felix Fröhlich, Mar 18 2022

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

Original entry on oeis.org

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

Felix Fröhlich, Apr 18 2015

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

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

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

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 *)

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

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

A257211 Numbers n such that the decimal expansions of both n and n^2 have 1 as smallest digit and 8 as largest digit.

Original entry on oeis.org

128, 178, 871, 1128, 1178, 1218, 1258, 1278, 1284, 1328, 1358, 1368, 1478, 1678, 1681, 1768, 1778, 1784, 1785, 1828, 1874, 1881, 2681, 2861, 2871, 3418, 3581, 3718, 3816, 3841, 4178, 4318, 4815, 4831, 4841, 4881, 5178, 5181, 5182, 5318, 5815, 5841, 5871, 5881

Offset: 1

Felix Fröhlich, Apr 18 2015

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

Cf. A256630, A256631, A256633, A256634, A256708, A256709, A256889, A257197, A257210, A256601.

fQ[n_] := Block[{d = DigitCount@ n}, Plus @@ Take[d, {9, 10}] == 0 && d[[1]] > 0 && d[[8]] > 0]; Select[Range@ 6000, fQ@ # && fQ[#^2] &] (* Michael De Vlieger, Apr 20 2015 *)
sd1ld8Q[n_]:=With[{idn=IntegerDigits[n]},Max[idn]==8&&Min[idn]==1]; Select[ Range[ 6000],AllTrue[{#,#^2},sd1ld8Q]&] (* Harvey P. Dale, Oct 14 2022 *)

is(n) = vecmin(digits(n))==1 && vecmin(digits(n^2))==1 && vecmax(digits(n))==8 && vecmax(digits(n^2))==8

A256601 Numbers n such that the decimal expansions of both n and n^2 have 1 as smallest digit and 9 as largest digit.

Original entry on oeis.org

139, 219, 519, 591, 719, 891, 911, 961, 971, 981, 1139, 1193, 1219, 1292, 1293, 1296, 1319, 1339, 1389, 1391, 1392, 1394, 1396, 1469, 1579, 1589, 1691, 1719, 1729, 1769, 1793, 1839, 1869, 1896, 1911, 1927, 1937, 1939, 1944, 1946, 1969, 1978, 1979, 1981, 1986

Offset: 1

Felix Fröhlich, Apr 20 2015

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

Cf. A256630, A256631, A256633, A256634, A256708, A256709, A256889, A257197, A257210, A257211.

fQ[n_] := Block[{d = DigitCount@ n}, Last@ d == 0 && d[[1]] > 0 && d[[9]] > 0]; Select[Range@ 2000, fQ@ # && fQ[#^2] &] (* Michael De Vlieger, Apr 20 2015 *)

is(n) = vecmin(digits(n))==1 && vecmin(digits(n^2))==1 && vecmax(digits(n))==9 && vecmax(digits(n^2))==9

cp's OEIS Frontend

A256631 Numbers n such that the decimal expansions of both n and n^2 have 0 as smallest digit and 5 as largest digit.

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A256633 Numbers n such that the decimal expansions of both n and n^2 have 0 as smallest digit and 6 as largest digit.

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A256630 Numbers n such that the decimal expansions of both n and n^2 have 0 as smallest digit and 4 as largest digit.

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A256634 Numbers n such that the decimal expansions of both n and n^2 have 0 as smallest digit and 7 as largest digit.

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A256709 Numbers n such that the decimal expansions of both n and n^2 have 0 as smallest digit and 9 as largest digit.

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A256889 Numbers k such that the decimal expansions of both k and k^2 have 1 as smallest digit and 5 as largest digit.

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A257197 Numbers k such that the decimal expansions of both k and k^2 have 1 as smallest digit and 6 as largest digit.

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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.

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A257211 Numbers n such that the decimal expansions of both n and n^2 have 1 as smallest digit and 8 as largest digit.