A333475 Numbers k such that S(2^k) is a perfect square, where S(t) is the sum of decimal digits of t.

0, 2, 16, 22, 36, 78, 104, 110, 118, 130, 176, 186, 194, 200, 216, 240, 270, 276, 320, 358, 364, 376, 440, 558, 576, 602, 608, 612, 614, 620, 630, 700, 872, 884, 894, 918, 972, 1144, 1174, 1192, 1216, 1536, 1566, 1610, 1658, 1798, 1882, 2000, 2312, 2630, 2928, 3042, 3540, 3648, 3744, 3750, 3774

Offset: 1

Author

Daniel Starodubtsev, Mar 23 2020

Keywords

• nonn
• base

Comments

Numbers k such that A000079(k) is in A028839.

All terms are even. - Robert Israel, Mar 24 2020

Examples

			16 is in the sequence, because S(2^16) = S(65536) = 25 is a perfect square.
		

Links

• Robert Israel, Table of n, a(n) for n = 1..209

Crossrefs

Cf. A000079, A007953, A028839.

Programs

Maple

sd:= n -> convert(convert(n,base,10),`+`):
select(t -> issqr(sd(2^t)), [$0..10000]); # Robert Israel, Mar 24 2020

PARI

isok(k) = issquare(sumdigits(2^k)); \\ Michel Marcus, Mar 23 2020