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A164771 Numbers n such that the average digit of n^2 is 1. 8

%I

%S 1,1049,1490,10002,10005,10011,10020,10050,10101,10110,10149,10200,

%T 10500,11001,11010,11100,11490,12000,14499,15000,17610,18000,20001,

%U 20010,20100,21000,24900,30000,33200,35000,36100,44900,44990,45100

%N Numbers n such that the average digit of n^2 is 1.

%C There are 117 such n's < 10^7: 1,1049,1490,10002,10005,10011,10020,10050,10101,10110,10149,10200,10500, 11001,11010,11100,11490,12000,14499,15000,17610,18000,20001,20010,20100, 21000,24900,30000,33200,35000,36100,44900,44990,45100,46000,54800,55000, 64900,71000,80000,1000006,1000015,1000051,1000055,1000060,1000105,1000150, 1000501,1000510,1000550,1000600,1001005,1001050,1001500,1005001,1005010, 1005100,1005500,1006000,1006490,1009951,1010005,1010050,1010149,1010500, 1011490,1015000,1024900,1050001,1050010,1050100,1051000,1055000,1060000, 1064900,1095500,1096000,1100005,1100050,1100500,1105000,1114900,1145000, 1150000,1190000,1224749,1244990,1249000,1414249,1415000,1420000,1424900, 1429000,1451000,1460000,1484251,1500001,1500010,1500100,1501000,1510000, 1550000,1600000,1735000,1739000,1789000,1820000,2000005,2000050,2000500, 2005000,2050000,2239000,2261000,2450000,2500000,2900000.

%C Or: Numbers n such that n is in A061384, i.e., square root of squares in A061384. - _M. F. Hasler_, Dec 05 2010

%F A055642(a(n)^2) = A007953(a(n)^2). - _M. F. Hasler_, Dec 05 2010

%e a(2)=1049 because 1049^2=1100401 and (1+1+0+0+4+0+1)/7=1.

%t Select[Range[50000],Mean[IntegerDigits[#^2]]==1&] (* _Harvey P. Dale_, Dec 15 2014 *)

%o (PARI) {for(d=1,9, for(n=sqrtint(10^(d-1)-1)+1, sqrtint(10^d-1), my(n2=divrem(n^2,10)); sum( k=2,d, (n2=divrem(n2[1],10))[2],n2[2])/d==1 & print1(n",")))} \\ _M. F. Hasler_, Dec 05 2010

%K base,nonn

%O 1,2

%A _Zak Seidov_, Aug 26 2009

%E Terms up to a(117) checked with given PARI code by _M. F. Hasler_, Dec 05 2010

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Last modified March 3 03:03 EST 2021. Contains 341756 sequences. (Running on oeis4.)