A262713 Numbers k such that the sum of digits of k^2 is 10.

8, 19, 35, 46, 55, 71, 80, 145, 152, 179, 190, 251, 332, 350, 361, 449, 451, 460, 548, 550, 649, 710, 800, 1450, 1520, 1790, 1900, 2510, 3320, 3500, 3610, 4490, 4499, 4510, 4600, 5480, 5500, 6490, 7100, 8000, 14500, 15200, 17900, 19000, 20249, 20251, 24499

Offset: 1

Author

Vincenzo Librandi, Sep 28 2015

Keywords

• nonn
• base

Comments

From Altug Alkan, Sep 29 2015: (Start)

Subsequence of A001651.

If a(n)+1 mod 9 != 0 then a(n)-1 mod 9 = 0;

if a(n)-1 mod 9 != 0 then a(n)+1 mod 9 = 0;

a(n)^2 - 1 mod 9 = 0. (End)

A135027(n)*10^k is a term for all n > 0, k >= 0. - Michael S. Branicky, Aug 19 2021

Examples

			19 is in sequence because 19^2 = 361 and 3+6+1 = 10.
		

Links

• Michael S. Branicky, Table of n, a(n) for n = 1..244
• Michael S. Branicky, Python program

Crossrefs

Cf. similar sequences listed in A262711.

Cf. A004159, A061910, A135027.

Programs

Magma

[n: n in [1..3*10^4] | &+Intseq(n^2) eq 10 ];

Mathematica

Select[Range[10^5], Total[IntegerDigits[#^2]] == 10 &]

PARI

for(n=1, 1e6, if (sumdigits(n^2) == 10, print1(n", "))) \\ Altug Alkan, Sep 28 2015

Python

# See linked program to go to larger numbers
def ok(n): return sum(map(int, str(n*n))) == 10
print(list(filter(ok, range(25000)))) # Michael S. Branicky, Aug 19 2021