A257485 -id:A257485 - cp's OEIS frontend

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

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

A257486 Numbers n such that the decimal expansions of both n and n^2 have 3 as smallest digit and 7 as largest digit.

Original entry on oeis.org

6734, 67434, 577734, 667334, 745356, 6674334, 6734744, 6756734, 7373376, 7453574, 7466434, 7533576, 66673334, 67345644, 67656734, 74547734, 74656376, 75733576, 666743334, 667335356, 746556344, 5775434474, 6666733334, 6666733576, 6676476434, 7447533576

Offset: 1

Felix Fröhlich, Apr 26 2015

Chai Wah Wu, Table of n, a(n) for n = 1..1000 (n = 71..178 from Giovanni Resta)

Cf. A137121, A256630, A256631, A256633, A256634, A256708, A256709, A256889, A257197, A257210, A257211, A256601, A257310, A249915, A257123, A257368, A257485.

fQ[n_] := Block[{d = DigitCount@ n}, Plus @@ Join[Take[d, {1, 2}], Take[d, {8, 10}]] == 0 && d[[3]] > 0 && d[[7]] > 0]; Select[Range@ 1000000, fQ@# && fQ[#^2] &] (* Michael De Vlieger, Apr 27 2015 *)

is(n) = vecmin(digits(n))==3 && vecmin(digits(n^2))==3 && vecmax(digits(n))==7 && vecmax(digits(n^2))==7

from itertools import product, repeat
A257486_list = []
for l in range(12):
    for a in product('34567',repeat = l):
        for b in ('4','5','6'):
            s = ''.join(a)+b
            if '3' in s and '7' in s:
                n = int(s)
                if {'3','7'} <= set(str(n**2)) <= {'3','4','5','6','7'}:
                    A257486_list.append(n) # Chai Wah Wu, May 02 2015

a(22)-a(26) from Hiroaki Yamanouchi, May 03 2015 (using Chai Wah Wu's b-file)

A257498 Numbers n such that the decimal expansions of both n and n^2 have 3 as the digit with the smallest value and 8 as the digit with the largest value.

Original entry on oeis.org

7378, 66834, 67438, 67738, 73874, 86356, 577378, 577438, 586374, 658388, 666834, 667438, 676438, 683874, 683876, 684438, 688374, 738474, 738538, 743878, 744538, 744738, 747378, 747438, 763844, 764438, 765738, 766384, 863388, 863474, 873874, 874378, 875434

Offset: 1

Felix Fröhlich, Apr 27 2015

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

Cf. A256630, A256631, A256633, A256634, A256708, A256709, A256889, A257197, A257210, A257211, A256601, A257310, A249915, A257123, A257368, A257485, A257486, A238553, A257534.

fQ[n_] := Block[{c = DigitCount@ n}, And[Plus @@ Take[c, {1, 2}] == 0, Plus @@ Take[c, {9, 10}] == 0, c[[3]] > 0, c[[8]] > 0]]; Select[Range@ 1000000, fQ@ # && fQ[#^2] &] (* Michael De Vlieger, May 05 2015 *)

is(n) = vecmin(digits(n))==3 && vecmin(digits(n^2))==3 && vecmax(digits(n))==8 && vecmax(digits(n^2))==8

A238553 Numbers n such that the decimal expansions of both n and n^2 have 3 as the digit with the smallest value and 9 as the digit with the largest value.

Original entry on oeis.org

5793, 5963, 6593, 6963, 7593, 8593, 9357, 9463, 9663, 9883, 9934, 9937, 9938, 57937, 58893, 58937, 58963, 59463, 59537, 59543, 59663, 59736, 59833, 59863, 59883, 65937, 66893, 68963, 69537, 69634, 69883, 73956, 73957, 79583, 79836, 79837, 79934, 83594, 85938

Offset: 1

Felix Fröhlich, Apr 27 2015

			5793 is in the sequence because its smallest digit is 3 and its largest digit is 9, and this is also true of 5793^2 = 33558849.
5833 is not in the sequence because 5833^2 = 34023889, which contains a 0 and a 2.

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

Cf. A256630, A256631, A256633, A256634, A256708, A256709, A256889, A257197, A257210, A257211, A256601, A257310, A249915, A257123, A257368, A257485, A257486, A257498, A257534, A254071, A254072, A254074.

fQ[n_] := Block[{c = DigitCount@ n}, And[Plus @@ Take[c, {1, 2}] == 0, Last@ c == 0, c[[3]] > 0, c[[9]] > 0]]; Select[Range@ 90000, fQ@ # && fQ[#^2] &] (* Michael De Vlieger, May 05 2015 *)

is(n) = vecmin(digits(n))==3 && vecmin(digits(n^2))==3 && vecmax(digits(n))==9 && vecmax(digits(n^2))==9

A254071 Numbers n such that the decimal expansions of both n and n^2 have 4 as the digit with the smallest value and 8 as the digit with the largest value.

Original entry on oeis.org

684, 6684, 8874, 66684, 68474, 74758, 76478, 86478, 666684, 668474, 675684, 744758, 766458, 6666684, 6668474, 6675684, 6748678, 6845784, 7586478, 8686574, 8875684, 66666684, 66756684, 74744758, 74758576, 75858874, 75867574, 76464878, 86878458, 87546878

Offset: 1

Felix Fröhlich, May 03 2015

Chai Wah Wu, Table of n, a(n) for n = 1..1000

Cf. A256630, A256631, A256633, A256634, A256708, A256709, A256889, A257197, A257210, A257211, A256601, A257310, A249915, A257123, A257368, A257485, A257486, A257498, A238553.

fQ[n_] := Block[{c = DigitCount@ n}, And[Plus @@ Take[c, {1, 3}] == 0, Plus @@ Take[c, {9, 10}] == 0, c[[4]] > 0, c[[8]] > 0]]; Select[Range@ 1000000, fQ@ # && fQ[#^2] &] (* Michael De Vlieger, May 05 2015 *)

is(n) = vecmin(digits(n))==4 && vecmin(digits(n^2))==4 && vecmax(digits(n))==8 && vecmax(digits(n^2))==8

A257534 Numbers n such that the decimal expansions of both n and n^2 have 4 as the digit with the smallest value and 7 as the digit with the largest value.

Original entry on oeis.org

74, 74476, 74474476

Offset: 1

Felix Fröhlich, Apr 28 2015

Subsequence of A136948 and of A137139.
a(4) > 10^19, if it exists. - Giovanni Resta, May 11 2015
From Jon E. Schoenfield, Jun 28 2015: (Start)
a(4) > 6.6666...*10^28, if it exists.
Define a property P1 such that, for any positive integer k, P1(k) is true iff the smallest- and largest-valued digits of the decimal expansion of k are 4 and 7, respectively. This sequence lists the positive integers n such that both P1(n) and P1(n^2) are true.
Define a less-restrictive property P2 such that, for any positive integer k, P2(k) is true iff the smallest- and largest-valued digits of the decimal expansion of k are at least 4 and at most 7, respectively. There exist only four positive integers n < 6.6666...*10^28, such that both P2(n) and P2(n^2) are true: a(1), a(2), a(3), and 76 (whose square, 5776, has minimum digit 5).
Conjecture: a(4) does not exist. (End)
a(4) > 7.44*10^36, if it exists. - Chai Wah Wu, Sep 09 2017

Cf. A136948, A137139.

Cf. A256630, A256631, A256633, A256634, A256708, A256709, A256889, A257197, A257210, A257211, A256601, A257310, A249915, A257123, A257368, A257485, A257486, A257498, A238553, A254071, A254072, A254074.

fQ[n_] := Block[{c = DigitCount@ n}, And[Plus @@ Take[c, {1, 3}] == 0, Plus @@ Take[c, {8, 10}] == 0, c[[4]] > 0, c[[7]] > 0]]; Select[Range@ 1000000, fQ@ # && fQ[#^2] &] (* Michael De Vlieger, May 05 2015 *)

is(n) = vecmin(digits(n))==4 && vecmin(digits(n^2))==4 && vecmax(digits(n))==7 && vecmax(digits(n^2))==7

A254072 Numbers n such that the decimal expansions of both n and n^2 have 4 as the digit with the smallest value and 9 as the digit with the largest value.

Original entry on oeis.org

974, 9476, 9874, 69684, 94588, 94657, 94788, 94867, 97457, 99476, 99784, 669684, 677974, 697764, 699684, 699764, 699784, 746957, 869457, 945857, 946878, 946888, 947457, 947574, 947886, 947887, 947976, 948678, 974457, 974474, 984878, 998784, 6669684, 6696684

Offset: 1

Felix Fröhlich, May 03 2015

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

Cf. A256630, A256631, A256633, A256634, A256708, A256709, A256889, A257197, A257210, A257211, A256601, A257310, A249915, A257123, A257368, A257485, A257486, A257498, A238553, A257534, A254071.

fQ[n_] := Block[{c = DigitCount@ n}, And[Plus @@ Take[c, {1, 3}] == 0, Last@ c == 0, c[[4]] > 0, c[[9]] > 0]]; Select[Range@ 1000000, fQ@ # && fQ[#^2] &] (* Michael De Vlieger, May 05 2015 *)

is(n) = vecmin(digits(n))==4 && vecmin(digits(n^2))==4 && vecmax(digits(n))==9 && vecmax(digits(n^2))==9

A254074 Numbers k such that the decimal expansions of both k and k^2 have 5 as the digit with the smallest value and 9 as the digit with the largest value.

Original entry on oeis.org

759576, 97759786, 97957576, 887579686, 987759576, 987859786, 7599859786, 7679576587, 8756697886, 8766958976, 9775989867, 9897756766, 9978965766, 76797588887, 88766997576, 97978858887, 99777685676, 99789658666, 99879856766, 767897685676, 869866586666

Offset: 1

Felix Fröhlich, May 03 2015

The first digit of a term is either 7, 8 or 9 and the last digit is either 5, 6 or 7. Conjecture: no term is a multiple of 5. - Chai Wah Wu, Sep 10 2017

Chai Wah Wu, Table of n, a(n) for n = 1..1224 (n = 1..326 from Hiroaki Yamanouchi).

Cf. A137147, A256630, A256631, A256633, A256634, A256708, A256709, A256889, A257197, A257210, A257211, A256601, A257310, A249915, A257123, A257368, A257485, A257486, A257498, A238553, A257534, A254071.

fQ[n_] := Block[{c = DigitCount@ n}, And[Plus @@ Take[c, {1, 4}] == 0, Last@ c == 0, c[[5]] > 0, c[[9]] > 0]]; Select[Range@ 10000000, fQ@ # && fQ[#^2] &] (* Michael De Vlieger, May 05 2015 *)

is(n) = vecmin(digits(n))==5 && vecmin(digits(n^2))==5 && vecmax(digits(n))==9 && vecmax(digits(n^2))==9

a(14)-a(21) from Hiroaki Yamanouchi, May 07 2015

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

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A257486 Numbers n such that the decimal expansions of both n and n^2 have 3 as smallest digit and 7 as largest digit.

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A257498 Numbers n such that the decimal expansions of both n and n^2 have 3 as the digit with the smallest value and 8 as the digit with the largest value.

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A238553 Numbers n such that the decimal expansions of both n and n^2 have 3 as the digit with the smallest value and 9 as the digit with the largest value.

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A254071 Numbers n such that the decimal expansions of both n and n^2 have 4 as the digit with the smallest value and 8 as the digit with the largest value.

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A257534 Numbers n such that the decimal expansions of both n and n^2 have 4 as the digit with the smallest value and 7 as the digit with the largest value.

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A254072 Numbers n such that the decimal expansions of both n and n^2 have 4 as the digit with the smallest value and 9 as the digit with the largest value.

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A254074 Numbers k such that the decimal expansions of both k and k^2 have 5 as the digit with the smallest value and 9 as the digit with the largest value.

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