A295008 -id:A295008 - cp's OEIS frontend

A295009 Numbers k such that the largest digit of k^2 is 9.

3, 7, 13, 14, 17, 23, 27, 30, 31, 33, 36, 37, 43, 44, 47, 53, 54, 57, 63, 64, 67, 70, 73, 77, 83, 86, 87, 89, 93, 95, 96, 97, 98, 99, 103, 107, 113, 114, 117, 118, 123, 127, 130, 133, 134, 136, 137, 138, 139, 140, 141, 143, 147, 148, 153, 157, 158, 161, 163, 164, 167, 170, 171

Offset: 1

M. F. Hasler, Nov 12 2017

			23 is in this sequence because 23^2 = 529 has 9 as largest digit.

Cf. A295019 (the corresponding squares), A277959 .. A277961 (same for digit 2 .. 4), A295005 .. A295008 (same for digit 5 .. 8).

Cf. A000290 (the squares).

select( is_A295009(n)=n&&vecmax(digits(n^2))==9 , [0..999]) \\ The "n&&" avoids an error message for n=0.

a(n) = sqrt(A295019(n)), where sqrt = A000196 or A000194 or A003059.

A295018 Squares whose largest digit is 8.

Original entry on oeis.org

81, 484, 784, 841, 1681, 3481, 3844, 5184, 6084, 8100, 8281, 8464, 8836, 10816, 11881, 14884, 15876, 16384, 18225, 22801, 25281, 28224, 28561, 31684, 33856, 36481, 36864, 38025, 38416, 40804, 43681, 48400, 48841, 53824, 58081, 58564, 67081, 68121, 68644, 71824, 77284, 77841, 78400

Offset: 1

M. F. Hasler, Nov 12 2017

Robert Israel, Table of n, a(n) for n = 1..10000

Cf. A295008 (square roots of the terms), A277946 - A277948 (same for digit 2..4), A295015 - A295019 (same for digit 5..9).

Cf. A000290 (the squares).

Res:= NULL: count:= 0:
for n from 1 while count < 50 do
  if max(convert(n^2,base,10))=8 then
    count:= count+1; Res:= Res, n^2;
  fi
od:
Res; # Robert Israel, Jul 21 2019

Select[Range[300]^2,Max[IntegerDigits[#]]==8&] (* Harvey P. Dale, Jul 08 2020 *)

is_A295018(n)=issquare(n)&&n&&vecmax(digits(n))==8 \\ "&&n" avoids an error message for n=0.

a(n) = A295008(n)^2.

A294998 Numbers n such that the largest digit of n^3 is 8.

Original entry on oeis.org

2, 12, 18, 20, 22, 24, 32, 35, 38, 42, 44, 47, 52, 53, 62, 72, 75, 82, 83, 87, 88, 92, 93, 94, 95, 96, 102, 104, 114, 115, 120, 122, 123, 127, 138, 141, 142, 145, 152, 153, 155, 161, 162, 172, 174, 180, 182, 183, 186, 192, 194, 195, 200, 201, 202, 203, 205, 206, 217, 220, 228, 232, 238, 240, 242, 244, 251

Offset: 1

M. F. Hasler, Nov 13 2017

For any term a(n), all numbers of the form a(n)*10^k, k >= 0, are in this sequence. We could call "primitive" the terms not of this form, i.e., without trailing '0'.

			12 is in the sequence because the largest digit of 12^3 = 1728 is 8.

Robert Israel, Table of n, a(n) for n = 1..10000

Cf. A295023 (the corresponding cubes); A278937, A294664, A294665, A294996 .. A294999 (same for digit 3, ..., 9); A295008 (same for squares).

Cf. A000578 (the cubes).

filter:= n -> max(convert(n^3,base,10))=8:
select(filter, [$1..1000]); # Robert Israel, Jul 03 2020

Select[Range[300],Max[IntegerDigits[#^3]]==8&] (* Harvey P. Dale, Aug 21 2019 *)

for(n=1,500, vecmax(digits(n^3))==8&&print1(n","))

cp's OEIS Frontend

A295009 Numbers k such that the largest digit of k^2 is 9.

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A295018 Squares whose largest digit is 8.

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Maple

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A294998 Numbers n such that the largest digit of n^3 is 8.

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Maple

Mathematica

PARI