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

%I A333475 #11 Mar 24 2020 17:18:24
%S A333475 0,2,16,22,36,78,104,110,118,130,176,186,194,200,216,240,270,276,320,
%T A333475 358,364,376,440,558,576,602,608,612,614,620,630,700,872,884,894,918,
%U A333475 972,1144,1174,1192,1216,1536,1566,1610,1658,1798,1882,2000,2312,2630,2928,3042,3540,3648,3744,3750,3774
%N A333475 Numbers k such that S(2^k) is a perfect square, where S(t) is the sum of decimal digits of t.
%C A333475 Numbers k such that A000079(k) is in A028839.
%C A333475 All terms are even. - _Robert Israel_, Mar 24 2020
%H A333475 Robert Israel, <a href="/A333475/b333475.txt">Table of n, a(n) for n = 1..209</a>
%e A333475 16 is in the sequence, because S(2^16) = S(65536) = 25 is a perfect square.
%p A333475 sd:= n -> convert(convert(n,base,10),`+`):
%p A333475 select(t -> issqr(sd(2^t)), [$0..10000]); # _Robert Israel_, Mar 24 2020
%o A333475 (PARI) isok(k) = issquare(sumdigits(2^k)); \\ _Michel Marcus_, Mar 23 2020
%Y A333475 Cf. A000079, A007953, A028839.
%K A333475 nonn,base
%O A333475 1,2
%A A333475 _Daniel Starodubtsev_, Mar 23 2020