A262713 - OEIS

%I #20 Sep 08 2022 08:46:14

%S 8,19,35,46,55,71,80,145,152,179,190,251,332,350,361,449,451,460,548,

%T 550,649,710,800,1450,1520,1790,1900,2510,3320,3500,3610,4490,4499,

%U 4510,4600,5480,5500,6490,7100,8000,14500,15200,17900,19000,20249,20251,24499

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

%C From _Altug Alkan_, Sep 29 2015: (Start)

%C Subsequence of A001651.

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

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

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

%C A135027(n)*10^k is a term for all n > 0, k >= 0. - _Michael S. Branicky_, Aug 19 2021

%H Michael S. Branicky, <a href="/A262713/b262713.txt">Table of n, a(n) for n = 1..244</a>

%H Michael S. Branicky, <a href="/A262713/a262713.txt">Python program</a>

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

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

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

%o (PARI) for(n=1, 1e6, if (sumdigits(n^2) == 10, print1(n", "))) \\ _Altug Alkan_, Sep 28 2015

%o (Python) # See linked program to go to larger numbers

%o def ok(n): return sum(map(int, str(n*n))) == 10

%o print(list(filter(ok, range(25000)))) # _Michael S. Branicky_, Aug 19 2021

%Y Cf. similar sequences listed in A262711.

%Y Cf. A004159, A061910, A135027.

%K nonn,base

%O 1,1

%A _Vincenzo Librandi_, Sep 28 2015