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

1,2

Comments

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

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

Links

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

Example

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

Maple

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

Prog

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

Crossrefs

Cf. A000079, A007953, A028839.

Sequence in context: A271627 A118954 A119599 * A330611 A228158 A330662

Adjacent sequences: A333472 A333473 A333474 * A333476 A333477 A333478

Keyword

nonn,base

Author

Daniel Starodubtsev, Mar 23 2020

Status

approved