A135027 -id:A135027 - cp's OEIS frontend

A226802 Primes p where the digital sum of p^2 is equal to 10.

19, 71, 179, 251, 449, 20249, 24499, 100549

Offset: 1

Vincenzo Librandi, Jun 24 2013

The next term is > 24154957 (if it exists). - R. J. Mathar, Jul 05 2013
No more terms below 10^12. - Hiroaki Yamanouchi, Sep 23 2014.
No additional terms < 10^15. - Chai Wah Wu, Nov 15 2015
No other terms below 10^50. The sequence is likely finite and complete. - Max Alekseyev, Jun 13 2025

			19 is in the sequence because 19^2=361 and 3+6+1=10.
71 is in the sequence because 71^2=5041 and 5+0+4+1=10.

Cf. A123157, A165492, A165459, A165493. Subset of A135027.

[p: p in PrimesUpTo(5*10^6) | &+Intseq(p^2) eq 10];

select(p -> isprime(p) and convert(convert(p^2,base,10),`+`)=10, [seq(2*k+1,k=1..100000)]); # Robert Israel, Sep 23 2014

Select[Prime[Range[70000]], Total[IntegerDigits[#^2]]== 10&]

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

Original entry on oeis.org

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

Vincenzo Librandi, Sep 28 2015

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

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

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

Cf. similar sequences listed in A262711.

Cf. A004159, A061910, A135027.

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

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

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

# 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

cp's OEIS Frontend

A226802 Primes p where the digital sum of p^2 is equal to 10.

Views

Author

Keywords

Comments

Examples

Crossrefs

Programs

Magma

Maple

Mathematica