A256889 -id:A256889 - 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

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

A257310 Numbers n such that the decimal expansions of both n and n^2 have 2 as smallest digit and 5 as largest digit.

Original entry on oeis.org

235, 2335, 23335, 233335, 2333335, 2354235, 23333335, 233333335, 2333333335, 2333524235, 23333333335, 23333524235, 233333333335, 2333333333335, 23333333333335, 233333333333335, 2333333333333335, 23333333333333335, 233333333333333335, 2333333333333333335

Offset: 1

Felix Fröhlich, Apr 20 2015

Conjecture: a(n) = A137066(n+2) for all n, i.e., this is A137066 without the initial two terms.

(10^(k+1)-1)/3 - 10^k + 2 are terms for k > 1. Conjecture: except for 2354235, 2333524235, and 23333524235, all terms are of this form. - Chai Wah Wu, Sep 10 2017

Chai Wah Wu, Table of n, a(n) for n = 1..40 (n = 1..31 from Hiroaki Yamanouchi)

Cf. A137066, A256630, A256631, A256633, A256634, A256708, A256709, A256889, A257197, A257210, A257211.

fQ[n_] := Block[{d = DigitCount@ n}, Plus @@ Prepend[Take[d, {6, 10}], First@ d] == 0 && d[[2]] > 0 && d[[5]] > 0]; Select[Range@ 1000000, fQ@ # && fQ[#^2] &] (* Michael De Vlieger, Apr 20 2015 *)

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

a(11)-a(20) from Hiroaki Yamanouchi, May 04 2015

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

Original entry on oeis.org

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

Felix Fröhlich, Apr 21 2015

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

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

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

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 *)

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

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

A257123 Numbers n such that the decimal expansions of both n and n^2 have 2 as smallest digit and 7 as largest digit.

Original entry on oeis.org

275, 2574, 2725, 2765, 4762, 5725, 6762, 7244, 7262, 23765, 25744, 27244, 27325, 27434, 27465, 27525, 27632, 27665, 47725, 52275, 52376, 52475, 52576, 52675, 57242, 67426, 72266, 72275, 72424, 72426, 72576, 72624, 73325, 73725, 74326, 75725, 233725, 233744

Offset: 1

Felix Fröhlich, Apr 25 2015

Felix Fröhlich, Table of n, a(n) for n = 1..1000

Cf. A137094, A256630, A256631, A256633, A256634, A256708, A256709, A256889, A257197, A257210, A257211, A256601, A257310, A249915, A257368, A257485, A257486, A257498, A257534.

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

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.

Views

Author

Keywords

Links

Crossrefs

Programs

Mathematica

PARI

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

Views

Author

Keywords

Links

Crossrefs

Programs

Mathematica

PARI

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

Views

Author

Keywords

Links

Crossrefs

Programs

Mathematica

PARI

Python

Extensions

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

Views

Author

Keywords

Links

Crossrefs

Programs

Mathematica

PARI

Extensions

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

Views

Author

Keywords

Comments

Links

Crossrefs

Programs

Mathematica

PARI

PARI

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

Views

Author

Keywords

Links

Crossrefs

Programs

Mathematica

PARI

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

Views

Author

Keywords

Links

Crossrefs

Programs

Mathematica

PARI

A257310 Numbers n such that the decimal expansions of both n and n^2 have 2 as smallest digit and 5 as largest digit.

Views

Author

Keywords

Comments

Links

Crossrefs

Programs

Mathematica

PARI

Extensions