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%I #26 Dec 01 2022 17:42:31
%S 1,2,4,8,512,68719476736,38685626227668133590597632,
%T 95780971304118053647396689196894323976171195136475136,
%U 25108406941546723055343157692830665664409421777856138051584,1606938044258990275541962092341162602522202993782792835301376
%N Powers of 2 with digit sum also a power of 2.
%C Question is the sequence finite or infinite?
%H Robert Israel, <a href="/A067499/b067499.txt">Table of n, a(n) for n = 1..13</a>
%F a(n) = 2^k with digit sum a(n) = 2^r.
%F { A000079 } intersect { A005349 }.
%e 512 = 2^9 and 5+1+2 = 8 = 2^3. 68719476736 = 2^36, sum of digits = 64 = 2^6.
%p with(numtheory): pow2 := [2^i$ i=1..2000]: for n from 1 to 1000 do L1 := convert(2^n, base, 10): if member(sum(L1[i], i=1..nops(L1)), pow2) then printf(`%d,`,2^n) fi: od: # _James A. Sellers_, Apr 19 2001
%t Select[Table[2^n,{n,0,250}],IntegerQ[Log[2,Total[IntegerDigits[#]]]] &] (* _Jayanta Basu_, May 19 2013 *)
%t Module[{nn=200,pw2},pw2=2^Range[0,nn];Select[pw2,MemberQ[pw2,Total[ IntegerDigits[ #]]]&]] (* _Harvey P. Dale_, Dec 01 2022 *)
%Y Subsequence of A000079, A005349.
%Y Cf. A095412.
%K base,nonn
%O 1,2
%A _Amarnath Murthy_, Apr 19 2001
%E More terms from _James A. Sellers_, Apr 19 2001
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