A316484 - OEIS

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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).

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

(list; graph; refs; listen; history; text; internal format)

OFFSET

1,1

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.)

LINKS

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

EXAMPLE

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.

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 *)

PROG

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

CROSSREFS

Cf. A056991, A069711, A316480.

Sequence in context: A280793 A160225 A377601 * A278794 A141090 A307580

Adjacent sequences: A316481 A316482 A316483 * A316485 A316486 A316487

KEYWORD

nonn,base

AUTHOR

Jon E. Schoenfield, Jul 04 2018

STATUS

approved