A165722 - OEIS

%I #31 Dec 15 2017 03:08:57

%S 1,2,3,4,5,6,7,10,12,13,14,17,18,23,37,43,46,60,119,183,223

%N Positive integers k such that the sum of decimal digits of (16^k - 1) equals 6*k.

%C Integers k such that A007953(16^k - 1) = A008588(k). - _Iain Fox_, Nov 22 2017

%C Conjecture: For k > 223, digsum(16^k - 1) < 6*k. This would mean that no further terms exist in the sequence. - _Iain Fox_, Nov 22 2017

%C No other terms below 10^6. - _Iain Fox_, Nov 25 2017

%C For all a(n), 2*a(n) is in A294652. - _Iain Fox_, Dec 02 2017

%e For k=1, 16-1 is 15 with sum of digits 6, so 1 is a term.

%e For k=2, 16^2-1 is 255 with sum of digits 12, so 2 is a term.

%t Select[Range[250],6#==Total[IntegerDigits[16^#-1]]&] (* _Harvey P. Dale_, Nov 13 2012 *)

%o (PARI) is(n) = 6*n == sumdigits(16^n-1) \\ _Iain Fox_, Nov 24 2017

%Y Cf. A007953, A294652.

%K base,more,nonn

%O 1,2

%A _Max Alekseyev_, Sep 24 2009