A295006 -id:A295006 - cp's OEIS frontend

A295005 Numbers n such that the largest digit of n^2 is 5.

5, 15, 35, 39, 45, 50, 55, 65, 71, 105, 112, 115, 145, 150, 155, 185, 188, 205, 211, 229, 235, 335, 350, 365, 368, 388, 389, 390, 450, 461, 485, 495, 500, 501, 502, 505, 550, 579, 585, 595, 635, 650, 652, 665, 671, 710, 711, 715, 718, 729, 735, 745, 1005, 1015, 1050

Offset: 1

M. F. Hasler, Nov 12 2017

			39 is in this sequence because 39^2 = 1521 has 5 as largest digit.

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

Cf. A295015 (the corresponding squares), A277959 .. A277961 (same for digit 2 .. 4), A295006 .. A295009 (same for digit 6 .. 9).

Cf. A000290 (the squares).

Select[Sqrt[ #]&/@(FromDigits/@Select[Tuples[ Range[ 0,5],7],Max[#] == 5&]),IntegerQ] (* Harvey P. Dale, Sep 23 2021 *)

select( is_A295005(n)=n&&vecmax(digits(n^2))==5 , [0..999]) \\ The "n&&" avoids an error message for n=0.

def aupto(limit):
  alst = []
  for k in range(1, limit+1):
    if max(str(k*k)) == "5": alst.append(k)
  return alst
print(aupto(1050)) # Michael S. Branicky, May 15 2021

a(n) = sqrt(A295015(n)), where sqrt = A000196 or A000194 or A003059.

A294996 Numbers n such that the largest digit of n^3 is 6.

Original entry on oeis.org

4, 6, 25, 36, 37, 40, 51, 60, 64, 77, 85, 86, 117, 118, 134, 136, 146, 154, 185, 218, 236, 250, 345, 360, 370, 374, 381, 384, 400, 405, 465, 510, 585, 586, 587, 600, 606, 625, 640, 705, 770, 805, 806, 825, 845, 850, 860, 1011, 1021, 1045, 1046, 1081, 1101, 1124, 1136, 1145, 1146, 1170, 1177, 1180

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'.

Includes a*10^k+b for k >= 3 and [a,b] in {[11, 1], [5, 4], [4, 5], [6, 5], [5, 6], [11, 10], [1, 11], [10, 11]}, and 8*10^k+8 for k >= 4. - Robert Israel, Jul 22 2019

			4 is in the sequence because the largest digit of 4^3 = 64 is 6.

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

Cf. A295021 (the corresponding cubes); A278937, A294664, A294665, A294997 .. A294999 (same for digit 3, ..., 9); A295006 (same for squares).

Cf. A000578 (the cubes).

for(n=1,2e3, vecmax(digits(n^3))==6&&print1(n","))

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.

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A295005 Numbers n such that the largest digit of n^2 is 5.

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A294996 Numbers n such that the largest digit of n^3 is 6.

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A295016 Squares whose largest digit is 6.

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