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

4, 1681, 3364, 3481, 4624, 7225, 9025, 1054729, 1069156, 1073296, 1149184, 1168561, 1183744, 1227664, 1263376, 1288225, 1308736, 1329409, 1366561, 1517824, 1522756, 1545049, 1567504, 1585081, 1607824, 1630729, 1635841, 1677025, 1682209, 1705636, 1729225

Offset: 1

Author

Jon E. Schoenfield, Jul 04 2018

Keywords

• nonn
• base

Comments

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.)

Examples

			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.
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.
		

Links

• Robert Israel, Table of n, a(n) for n = 1..10000

Crossrefs

Cf. A056991, A069711, A316480.

Programs

Maple

f:= proc(n) local L;
  L:= convert(n^2,base,10);
  if convert(L,`+`)=4*nops(L) then n^2 fi
end proc:
map(f, [$1..2000]); # Robert Israel, Jul 05 2018

Mathematica

Select[Range[1500]^2, Mean[IntegerDigits[#]] == 4 &] (* Giovanni Resta, Jul 05 2018 *)

PARI

isok(n) = (n>0) && issquare(n) && (sumdigits(n) == 4*#digits(n)); \\ Michel Marcus, Jul 05 2018