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

Author

M. F. Hasler, Nov 12 2017

Keywords

• nonn
• base

Examples

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

Links

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

Crossrefs

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

Cf. A000290 (the squares).

Programs

Mathematica

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

PARI

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

Python

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

Formula

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