A277948 -id:A277948 - cp's OEIS frontend

A277946 Squares whose largest decimal digit is 2.

121, 10201, 12100, 22201, 1002001, 1020100, 1022121, 1210000, 1212201, 2220100, 100020001, 100200100, 100220121, 102010000, 102212100, 121000000, 121022001, 121220100, 210221001, 222010000, 10000200001, 10002000100, 10002200121, 10020010000, 10020210201

Offset: 1

Colin Barker, Nov 05 2016

A subsequence of A000290.
From Robert Israel, Nov 14 2016: (Start)
If n is a term, then so is 100*n.
The first term with an even number of digits is a(36) = 100021020121.
The first term with an even number of digits that is not of the form a(36)*100^k has at least 24 digits.
(End)

Chai Wah Wu, Table of n, a(n) for n = 1..10000 (terms n = 1..50 from Colin Barker, terms n = 51..474 from Robert Israel)

Cf. A000290, A277947, A277948, A277959.

[n^2: n in [1..1000000] | Maximum(Intseq(n^2)) eq 2]; // Vincenzo Librandi, Nov 06 2016

res:= NULL: B:= [1,2]:
for m from 1 to 10 do
  for q in B do
    for x from ceil(sqrt(10^m*q)) to floor(sqrt(10^m*q + 2/9*(10^m-1))) do
      if max(convert(x^2,base,10)) = 2 then res:= res, x^2 fi
  od od:
  for q in B do
     for x from ceil(sqrt(10^(m+1)*q)) to floor(sqrt(10^(m+1)*q + 2/9*(10^(m+1)-1))) do
       if max(convert(x^2,base,10)) = 2 then res:= res, x^2 fi
  od od:
  if m < 10 then B:= map(t -> (10*t,10*t+1,10*t+2),B) fi;
od:
res; # Robert Israel, Nov 14 2016

fQ[n_] := Union[ IntegerDigits[ n^2]][[-1]] == 2; Select[ Range@100500, fQ]^2 (* Robert G. Wilson v, Nov 06 2016 *)

L=List(); for(n=1, 10000, if(vecmax(digits(n^2))==2, listput(L, n^2))); Vec(L)
\\ See A277959 for more efficient code. - M. F. Hasler, Nov 16 2017

a(n) = A277959(n)^2. Intersection of A000290 and A277964. - M. F. Hasler, Nov 15 2017

A277961 Numbers n such that 4 is the largest decimal digit of n^2.

Original entry on oeis.org

2, 12, 18, 20, 21, 32, 38, 48, 49, 102, 120, 152, 179, 180, 182, 200, 201, 210, 318, 320, 321, 332, 338, 348, 362, 380, 451, 452, 462, 480, 482, 490, 548, 549, 649, 1002, 1012, 1020, 1021, 1049, 1102, 1111, 1188, 1200, 1201, 1429, 1488, 1498, 1518, 1520

Offset: 1

Colin Barker, Nov 06 2016

The actual squares are listed in A277948. - M. F. Hasler, Nov 12 2017
Includes 2*10^n+10^m for all n <> m. - Robert Israel, Nov 13 2017
For any term of q digits, the first m digits don't exceed (2 * 10^m - 2) / 3 = 666..66 (m 6's) for 1 <= m <= q. - David A. Corneth, Nov 13 2017
A term a(n) is in the sequence if and only if a(n)*10^k is in the sequence, for all k >= 0. If a(n) = (x*10^k + y)*10^m with 2xy < 10^k, then (y*10^k+x)*10^m' is also in the sequence, for all m'. - M. F. Hasler, Nov 13 2017

Colin Barker, Table of n, a(n) for n = 1..1000

Cf. A277948, A277959, A277960.

select(n -> max(convert(n^2,base,10))=4, [$1..10000]); # Robert Israel, Nov 13 2017

L=List(); for(n=1, 10000, if(vecmax(digits(n^2))==4, listput(L, n))); Vec(L)

a(n) = sqrt(A277948(n)), where sqrt = A000196 or A000194 or A003059. - M. F. Hasler, Nov 12 2017

A277947 Squares whose largest decimal digit is 3.

Original entry on oeis.org

12321, 123201, 130321, 1232100, 1320201, 3101121, 12320100, 13032100, 102030201, 102232321, 103002201, 123210000, 123232201, 132020100, 310112100, 1232010000, 1303210000, 1322122321, 1332323001, 2103231321, 10022212321, 10130221201, 10203020100, 10203222121

Offset: 1

Colin Barker, Nov 05 2016

A subsequence of A000290.

Colin Barker, Table of n, a(n) for n = 1..100

Cf. A000290.

Cf. A277946, A277948, A277960.

[n^2: n in [1..1000000] | Maximum(Intseq(n^2)) eq 3]; // Vincenzo Librandi, Nov 06 2016

L=List(); for(n=1, 10000, if(vecmax(digits(n^2))==3, listput(L, n^2))); Vec(L)

A294663 Cubes whose largest digit is 4.

Original entry on oeis.org

343, 314432, 343000, 34012224, 314432000, 343000000, 34012224000, 314432000000, 343000000000, 442102433032, 30304210142233, 34012224000000, 143121324002112, 314432000000000, 333014302331144, 343000000000000, 442102433032000, 30304210142233000, 34012224000000000

Offset: 1

M. F. Hasler, Nov 12 2017

For any term a(n), all numbers of the form a(n)*10^3k, k >= 0, are in this sequence. Primitive terms, i.e., not of this form (or equivalently: without trailing '0'), are 343, 314432, 34012224, 442102433032, 30304210142233, 143121324002112, 333014302331144, ...

			343 is in the sequence because it is a cube, 343 = 7^3, and its largest digit is 4.

Cf. A294664 (the corresponding cubic roots).
Cf. A277948 = A277961^2 (analog for squares).
Cf. A278936, A295025, A295021, ..., A295024 (analog for digits 3, 5, 6, ..., 9).
Cf. A000578 (the cubes).

for(n=1,2e8, vecmax(digits(n^3))==4&&print1(n^3,","))

a(n) = A294664(n)^3.

A295015 Squares whose largest digit is 5.

Original entry on oeis.org

25, 225, 1225, 1521, 2025, 2500, 3025, 4225, 5041, 11025, 12544, 13225, 21025, 22500, 24025, 34225, 35344, 42025, 44521, 52441, 55225, 112225, 122500, 133225, 135424, 150544, 151321, 152100, 202500, 212521, 235225, 245025, 250000, 251001, 252004, 255025, 302500

Offset: 1

M. F. Hasler, Nov 12 2017

Michael S. Branicky, Table of n, a(n) for n = 1..10000

Cf. A295015 (square roots of the terms); A277946, A277947, A277948, A295016 .. A295019 (analog for digits 2 through 9); A295025 (analog for cubes).

Cf. A000290 (the squares).

Select[Range[600]^2,Max[IntegerDigits[#]]==5&] (* Harvey P. Dale, Aug 19 2022 *)

is_A295015(n)=issquare(n)&&n&&vecmax(digits(n))==5 \\ The "n&&" avoids an error message for n = 0.

from math import isqrt
def aupto(limit):
  alst, rootlimit = [], isqrt(limit)
  for k in range(1, rootlimit+1):
    if max(str(k*k)) == "5": alst.append(k*k)
  return alst
print(aupto(302500)) # Michael S. Branicky, May 15 2021

a(n) = A295005(n)^2.

A295019 Squares whose largest digit is 9.

Original entry on oeis.org

9, 49, 169, 196, 289, 529, 729, 900, 961, 1089, 1296, 1369, 1849, 1936, 2209, 2809, 2916, 3249, 3969, 4096, 4489, 4900, 5329, 5929, 6889, 7396, 7569, 7921, 8649, 9025, 9216, 9409, 9604, 9801, 10609, 11449, 12769, 12996, 13689, 13924, 15129, 16129, 16900, 17689, 17956, 18496, 18769

Offset: 1

M. F. Hasler, Nov 12 2017

Cf. A295009 (square roots of the terms), A277946 - A277948 (same for digit 2..4), A295015 - A295018 (same for digit 5..8).

Cf. A000290 (the squares).

Select[Range[150]^2,Max[IntegerDigits[#]]==9&] (* Harvey P. Dale, Oct 27 2019 *)

is_A295019(n)=issquare(n)&&n&&vecmax(digits(n))==9 \\ "&&n" avoids an error message for n=0.

a(n) = A295009(n)^2.

A295016 Squares whose largest digit is 6.

Original entry on oeis.org

16, 36, 64, 256, 361, 625, 1156, 1600, 2116, 2601, 3136, 3364, 3600, 4356, 4624, 5625, 6241, 6400, 6561, 11236, 11664, 13456, 14161, 14641, 15625, 16641, 20164, 21316, 24336, 25600, 26244, 30625, 36100, 41616, 42436, 43264, 46225, 46656, 50625, 53361, 56644, 60025, 60516, 61504

Offset: 1

M. F. Hasler, Nov 12 2017

Harvey P. Dale, Table of n, a(n) for n = 1..1000

Cf. A295006 (square roots of the terms); A277946, A277947, A277948, A295015 .. A295019 (analog for digits 2 through 9), A295021 (analog for cubes).

Cf. A000290 (the squares).

Select[Range[250]^2,Max[IntegerDigits[#]]==6&] (* Harvey P. Dale, Jun 14 2025 *)

is_A295016(n)=issquare(n)&&n&&vecmax(digits(n))==6 \\ The "n&&" avoids an error message for n = 0.

a(n) = A295006(n)^2.

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.

A295017 Squares whose largest digit is 7.

Original entry on oeis.org

576, 676, 1764, 2704, 3721, 4761, 5476, 5776, 6724, 7056, 7225, 7744, 15376, 17161, 17424, 20736, 23716, 27225, 27556, 30276, 32761, 35721, 37636, 47524, 50176, 51076, 54756, 57121, 57600, 67600, 70225, 70756, 72361, 73441, 75076, 75625, 76176, 101761, 106276, 126736, 137641, 141376

Offset: 1

M. F. Hasler, Nov 12 2017

Harvey P. Dale, Table of n, a(n) for n = 1..1000

Cf. A295007 (square roots of the terms), A277946 .. A277948 (same for digit 2 .. 4), A295015 .. A295019 (same for digit 5 .. 9), A295022 (same for cubes).

Cf. A000290 (the squares).

Select[Range[1000]^2,Max[IntegerDigits[#]]==7&] (* Harvey P. Dale, Dec 15 2024 *)

is_A295017(n)=issquare(n)&&n&&vecmax(digits(n))==7 \\ The "n&&" avoids an error message for n=0.

a(n) = A295007(n)^2.

cp's OEIS Frontend

A277946 Squares whose largest decimal digit is 2.

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A277961 Numbers n such that 4 is the largest decimal digit of n^2.

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A277947 Squares whose largest decimal digit is 3.

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A294663 Cubes whose largest digit is 4.

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A295015 Squares whose largest digit is 5.

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A295019 Squares whose largest digit is 9.

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A295016 Squares whose largest digit is 6.

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A295018 Squares whose largest digit is 8.

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