cp's OEIS Frontend

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

%I A262713 #20 Sep 08 2022 08:46:14
%S A262713 8,19,35,46,55,71,80,145,152,179,190,251,332,350,361,449,451,460,548,
%T A262713 550,649,710,800,1450,1520,1790,1900,2510,3320,3500,3610,4490,4499,
%U A262713 4510,4600,5480,5500,6490,7100,8000,14500,15200,17900,19000,20249,20251,24499
%N A262713 Numbers k such that the sum of digits of k^2 is 10.
%C A262713 From _Altug Alkan_, Sep 29 2015: (Start)
%C A262713 Subsequence of A001651.
%C A262713 If a(n)+1 mod 9 != 0 then a(n)-1 mod 9 = 0;
%C A262713 if a(n)-1 mod 9 != 0 then a(n)+1 mod 9 = 0;
%C A262713 a(n)^2 - 1 mod 9 = 0. (End)
%C A262713 A135027(n)*10^k is a term for all n > 0, k >= 0. - _Michael S. Branicky_, Aug 19 2021
%H A262713 Michael S. Branicky, <a href="/A262713/b262713.txt">Table of n, a(n) for n = 1..244</a>
%H A262713 Michael S. Branicky, <a href="/A262713/a262713.txt">Python program</a>
%e A262713 19 is in sequence because 19^2 = 361 and 3+6+1 = 10.
%t A262713 Select[Range[10^5], Total[IntegerDigits[#^2]] == 10 &]
%o A262713 (Magma) [n: n in [1..3*10^4] | &+Intseq(n^2) eq 10 ];
%o A262713 (PARI) for(n=1, 1e6, if (sumdigits(n^2) == 10, print1(n", "))) \\ _Altug Alkan_, Sep 28 2015
%o A262713 (Python) # See linked program to go to larger numbers
%o A262713 def ok(n): return sum(map(int, str(n*n))) == 10
%o A262713 print(list(filter(ok, range(25000)))) # _Michael S. Branicky_, Aug 19 2021
%Y A262713 Cf. similar sequences listed in A262711.
%Y A262713 Cf. A004159, A061910, A135027.
%K A262713 nonn,base
%O A262713 1,1
%A A262713 _Vincenzo Librandi_, Sep 28 2015