login
A067499
Powers of 2 with digit sum also a power of 2.
14
1, 2, 4, 8, 512, 68719476736, 38685626227668133590597632, 95780971304118053647396689196894323976171195136475136, 25108406941546723055343157692830665664409421777856138051584, 1606938044258990275541962092341162602522202993782792835301376
OFFSET
1,2
COMMENTS
Question is the sequence finite or infinite?
LINKS
FORMULA
a(n) = 2^k with digit sum a(n) = 2^r.
{ A000079 } intersect { A005349 }.
EXAMPLE
512 = 2^9 and 5+1+2 = 8 = 2^3. 68719476736 = 2^36, sum of digits = 64 = 2^6.
MAPLE
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
MATHEMATICA
Select[Table[2^n, {n, 0, 250}], IntegerQ[Log[2, Total[IntegerDigits[#]]]] &] (* Jayanta Basu, May 19 2013 *)
Module[{nn=200, pw2}, pw2=2^Range[0, nn]; Select[pw2, MemberQ[pw2, Total[ IntegerDigits[ #]]]&]] (* Harvey P. Dale, Dec 01 2022 *)
CROSSREFS
Subsequence of A000079, A005349.
Cf. A095412.
Sequence in context: A013553 A302864 A061089 * A135212 A012456 A071686
KEYWORD
base,nonn
AUTHOR
Amarnath Murthy, Apr 19 2001
EXTENSIONS
More terms from James A. Sellers, Apr 19 2001
STATUS
approved