A256633 -id:A256633 - cp's OEIS frontend

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.

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

A257085 Numbers n such that the decimal expansions of both n and n^2 only use the digits 0..6.

Original entry on oeis.org

0, 1, 2, 4, 5, 6, 10, 11, 12, 15, 16, 20, 21, 25, 32, 34, 35, 40, 45, 46, 50, 51, 55, 56, 60, 65, 66, 100, 101, 102, 105, 106, 110, 111, 112, 115, 116, 120, 121, 125, 142, 145, 146, 150, 152, 155, 156, 160, 162, 200, 201, 204, 205, 206, 210, 211, 215, 216, 225, 231, 235, 245, 246, 250, 251, 252, 254, 255, 256

Offset: 1

Danny Rorabaugh, Apr 15 2015

			116 is in the list because 116 and 116^2 = 13456 do not use the digits 7, 8 or 9.
182 is not in the list because it uses the digit 8 (even though 182^2 = 33124 would be fine).
253 is not in the list because 253^2 = 6409 uses the digit 9.

Danny Rorabaugh, Table of n, a(n) for n = 1..10000

Cf. A178501 (0..1), A136808(0..2), A136809(0..3), A136810 (0..4), A257086 (0..5).

Cf. A136859, A256633.

Select[Range@ 256, Total@ Take[DigitCount[#], {7, 9}] == 0 && Total@ Take[DigitCount[#^2], {7, 9}] == 0 &] (* Michael De Vlieger, Apr 17 2015 *)

isok(n) = ((vecmax(digits(n)) <= 6) && (vecmax(digits(n^2)) <= 6)) || (n==0); \\ Michel Marcus, Feb 02 2016

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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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A257085 Numbers n such that the decimal expansions of both n and n^2 only use the digits 0..6.

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