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A316484 Squares whose arithmetic mean of digits is 4 (i.e., the sum of digits is 4 times the number of digits).

%I A316484 #18 Jul 06 2018 10:56:24
%S A316484 4,1681,3364,3481,4624,7225,9025,1054729,1069156,1073296,1149184,
%T A316484 1168561,1183744,1227664,1263376,1288225,1308736,1329409,1366561,
%U A316484 1517824,1522756,1545049,1567504,1585081,1607824,1630729,1635841,1677025,1682209,1705636,1729225
%N A316484 Squares whose arithmetic mean of digits is 4 (i.e., the sum of digits is 4 times the number of digits).
%C A316484 Each term's number of digits is in A056991 (Numbers with digital root 1, 4, 7, or 9). For every term k in A056991, this sequence contains at least one k-digit term. (See A316480.)
%H A316484 Robert Israel, <a href="/A316484/b316484.txt">Table of n, a(n) for n = 1..10000</a>
%e A316484 1027^2 + 1054729, a 7-digit number whose digit sum is 1+0+5+4+7+2+9 = 28 = 4*7, so 1054729 is a term.
%e A316484 10044^2 = 100881936, a 9-digit number whose digit sum is 1+0+0+8+8+1+9+3+6 = 36 = 4*9, so 100881936 is a term.
%p A316484 f:= proc(n) local L;
%p A316484   L:= convert(n^2,base,10);
%p A316484   if convert(L,`+`)=4*nops(L) then n^2 fi
%p A316484 end proc:
%p A316484 map(f, [$1..2000]); # _Robert Israel_, Jul 05 2018
%t A316484 Select[Range[1500]^2, Mean[IntegerDigits[#]] == 4 &] (* _Giovanni Resta_, Jul 05 2018 *)
%o A316484 (PARI) isok(n) = (n>0) && issquare(n) && (sumdigits(n) == 4*#digits(n)); \\ _Michel Marcus_, Jul 05 2018
%Y A316484 Cf. A056991, A069711, A316480.
%K A316484 nonn,base
%O A316484 1,1
%A A316484 _Jon E. Schoenfield_, Jul 04 2018