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A135027 Numbers k such that the sum of the digits of k^2 is 10. Multiples of 10 are omitted.

%I A135027 #22 May 30 2021 22:05:42
%S A135027 8,19,35,46,55,71,145,152,179,251,332,361,449,451,548,649,4499,20249,
%T A135027 20251,24499,100549,114499,316261
%N A135027 Numbers k such that the sum of the digits of k^2 is 10. Multiples of 10 are omitted.
%C A135027 A subsequence of A056020. - _R. J. Mathar_, Feb 10 2008
%C A135027 Next term > 10000000. - _R. J. Mathar_, Oct 20 2009
%C A135027 If it exists, a(24) > 10^10. - _Hugo Pfoertner_, May 17 2021
%C A135027 If it exists, a(24) > 10^29. - _Michael S. Branicky_, May 30 2021
%H A135027 Michael S. Branicky, <a href="/A135027/a135027.txt">Python program</a>
%e A135027 Corresponding squares are 64, 361, 1225, 2116, 3025, 5041, 21025, 23104, 32041, 63001, 110224, 130321, 201601, 203401, 300304, 421201, 20241001, 410022001, 410103001, 600201001, 10110101401, 13110021001, 100021020121.
%e A135027 8^2 = 64 and 6+4 = 10. 316261^2 = 100021020121 and 1+0+0+0+2+1+0+2+0+1+2+1 = 10. - _Zak Seidov_, Aug 26 2009
%t A135027 s={};Do[If[Mod[n,10]>0&&10==Total[IntegerDigits[n^2]],AppendTo[s,n]], {n,10^8}];s (* _Zak Seidov_, Aug 26 2009 *)
%o A135027 (Python)
%o A135027 def A007953(n):
%o A135027     a=0
%o A135027     sh=n
%o A135027     while sh > 0:
%o A135027         a += sh % 10
%o A135027         sh //= 10
%o A135027     return a
%o A135027 def isA135027(n):
%o A135027     if n % 10 == 0:
%o A135027         return False
%o A135027     else:
%o A135027         return A007953(n**2) == 10
%o A135027 for n in range(70000):
%o A135027     if isA135027(n):
%o A135027         print(n)
%o A135027 # _R. J. Mathar_, Oct 20 2009
%o A135027 (Python) # See linked program to go to large numbers
%o A135027 def ok(n): return n%10 != 0 and sum(map(int, str(n*n))) == 10
%o A135027 print(list(filter(ok, range(316262)))) # _Michael S. Branicky_, May 30 2021
%o A135027 (PARI) is(n) = sumdigits(n^2)==10 && n%10 > 0 \\ _Felix Fröhlich_, May 17 2021
%Y A135027 Cf. A007953, A056020.
%K A135027 base,more,nonn
%O A135027 1,1
%A A135027 _Zak Seidov_, Feb 10 2008