cp's OEIS Frontend

A095412 Exponents k such that the sum of decimal digits of 2^k is also a power of 2.

%I A095412 #34 Nov 25 2022 22:16:30
%S A095412 0,1,2,3,9,36,85,176,194,200,375,1517,1523,3042,5953,6043,6109,12068,
%T A095412 12104,96251,193734,386797,387589,1545477,3092224,3098800,6188717,
%U A095412 6191693,6199469,24753865,99084345
%N A095412 Exponents k such that the sum of decimal digits of 2^k is also a power of 2.
%e A095412 2^9 = 512 with digit sum = 8;
%e A095412 2^36 = 68719476736 with digit sum = 64;
%e A095412 2^85 = 38685626227668133590597632 with digit sum = 128;
%e A095412 2^96251 has a decimal digit sum of 131072.
%t A095412 Do[If[IntegerQ[Log[2, Plus@@IntegerDigits[2^n]]], Print[n] ], {n, 0, 10^6}];
%o A095412 (PARI) isp(n) = (n==1) || (n==2) || (ispower(n,,&k) && (k==2));
%o A095412 isok(n) = isp(sumdigits(2^n)); \\ _Michel Marcus_, Apr 25 2017
%Y A095412 Cf. A001370 (sum of digits of 2^n).
%K A095412 nonn,base,more
%O A095412 1,3
%A A095412 _Labos Elemer_, Jun 21 2004
%E A095412 More terms from _Ryan Propper_, Jun 13 2006
%E A095412 a(21)-a(23) from _Ray Chandler_, Jun 16 2006
%E A095412 a(24)-a(29) from _Jon E. Schoenfield_, Jul 22 2006
%E A095412 a(30) from _Giovanni Resta_, Apr 24 2017
%E A095412 a(31) from _Bert Dobbelaere_, Feb 22 2019
%E A095412 Offset corrected by _Jon E. Schoenfield_, Nov 25 2022