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

0, 1, 2, 3, 9, 36, 85, 176, 194, 200, 375, 1517, 1523, 3042, 5953, 6043, 6109, 12068, 12104, 96251, 193734, 386797, 387589, 1545477, 3092224, 3098800, 6188717, 6191693, 6199469, 24753865, 99084345

Offset: 1

Author

Labos Elemer, Jun 21 2004

Keywords

• nonn
• base
• more

Examples

			2^9 = 512 with digit sum = 8;
2^36 = 68719476736 with digit sum = 64;
2^85 = 38685626227668133590597632 with digit sum = 128;
2^96251 has a decimal digit sum of 131072.
		

Crossrefs

Cf. A001370 (sum of digits of 2^n).

Programs

Mathematica

Do[If[IntegerQ[Log[2, Plus@@IntegerDigits[2^n]]], Print[n] ], {n, 0, 10^6}];

PARI

isp(n) = (n==1) || (n==2) || (ispower(n,,&k) && (k==2));
isok(n) = isp(sumdigits(2^n)); \\ Michel Marcus, Apr 25 2017

Extensions

More terms from Ryan Propper, Jun 13 2006

a(21)-a(23) from Ray Chandler, Jun 16 2006

a(24)-a(29) from Jon E. Schoenfield, Jul 22 2006

a(30) from Giovanni Resta, Apr 24 2017

a(31) from Bert Dobbelaere, Feb 22 2019

Offset corrected by Jon E. Schoenfield, Nov 25 2022