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A260702 Numbers n such that 3*n and n^2 have the same digit sum.

%I A260702 #25 Sep 08 2022 08:46:13
%S A260702 0,3,6,9,12,15,18,21,30,33,39,45,48,51,60,66,90,96,99,102,105,111,120,
%T A260702 123,129,132,150,153,156,159,162,165,180,189,195,198,201,210,225,231,
%U A260702 246,252,255,261,285,300,330,333,348,351,390,399,429,450,453,459,462
%N A260702 Numbers n such that 3*n and n^2 have the same digit sum.
%C A260702 All terms are multiple of 3.
%C A260702 If n is in the sequence, then so is 10*n. - _Robert Israel_, Apr 05 2020
%H A260702 Robert Israel, <a href="/A260702/b260702.txt">Table of n, a(n) for n = 1..10000</a>
%F A260702 A007953(A008585(a(n))) = A007953(A000290(a(n))).
%e A260702 159 is in the sequence because 159^2 = 25281 and 3*159 = 477 have the same digit sum: 18.
%p A260702 select(n -> convert(convert(3*n,base,10),`+`)=convert(convert(n^2,base,10),`+`), [seq(i,i=0..1000,3)]); # _Robert Israel_, Apr 05 2020
%t A260702 Select[Range[0, 500], Total[IntegerDigits[3 #]] == Total[IntegerDigits[#^2]] &]
%o A260702 (Magma) [n: n in [0..500] | &+Intseq(3*n) eq &+Intseq(n^2)];
%o A260702 (PARI) isok(n) = sumdigits(3*n) == sumdigits(n^2); \\ _Michel Marcus_, Nov 17 2015
%o A260702 (Sage) [n for n in (0..500) if sum((3*n).digits())==sum((n^2).digits())] # _Bruno Berselli_, Nov 17 2015
%Y A260702 Cf. A000290, A007953, A008585, A049343, A058369.
%Y A260702 Contains A133384 and A199682.
%K A260702 nonn,base,easy
%O A260702 1,2
%A A260702 _Vincenzo Librandi_, Nov 17 2015