A257197 -id:A257197 - cp's OEIS frontend

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

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

A257368 Numbers n such that the decimal expansions of both n and n^2 have 2 as smallest digit and 8 as largest digit.

Original entry on oeis.org

278, 528, 582, 826, 2385, 2585, 2868, 2872, 2875, 2878, 2885, 4782, 4832, 4872, 5278, 5328, 6872, 7238, 7258, 7268, 7582, 8232, 8266, 8275, 8278, 8284, 8522, 8524, 8528, 8628, 8732, 8822, 23385, 23628, 23782, 23826, 25582, 25668, 25785, 25856, 26238, 26878

Offset: 1

Felix Fröhlich, Apr 25 2015

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

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

fQ[n_] := Block[{d = DigitCount@ n}, Plus @@ Prepend[Take[d, -2], First@ d] == 0 && d[[2]] > 0 && d[[8]] > 0]; Select[Range@ 27000, fQ@ # && fQ[#^2] &] (* Michael De Vlieger, Apr 27 2015 *)

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

A257485 Numbers n such that the decimal expansions of both n and n^2 have 2 as smallest digit and 9 as largest digit.

Original entry on oeis.org

927, 962, 982, 2293, 2393, 2593, 2693, 2792, 2923, 2927, 2932, 2937, 2964, 2973, 2977, 2982, 2983, 4792, 4923, 4927, 5692, 6292, 6923, 6925, 6927, 7923, 7924, 7927, 8792, 8925, 9232, 9233, 9267, 9268, 9273, 9286, 9287, 9288, 9325, 9326, 9327, 9342, 9423, 9427

Offset: 1

Felix Fröhlich, Apr 26 2015

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.

fQ[n_] := Block[{d = DigitCount@ n}, Plus @@ Join[First@ d, Last@ d] == 0 && d[[2]] > 0 && d[[9]] > 0]; Select[Range@ 10000, fQ@ # && fQ[#^2] &] (* Michael De Vlieger, Apr 27 2015 *)
s2l9Q[n_]:=Max[IntegerDigits[n]]==9&&Min[IntegerDigits[n]]==2; Select[ Range[ 10000],AllTrue[{#,#^2},s2l9Q]&] (* Harvey P. Dale, Dec 06 2018 *)

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

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

cp's OEIS Frontend

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.

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

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

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

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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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A257368 Numbers n such that the decimal expansions of both n and n^2 have 2 as smallest digit and 8 as largest digit.

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A257485 Numbers n such that the decimal expansions of both n and n^2 have 2 as smallest digit and 9 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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