A165722 Positive integers k such that the sum of decimal digits of (16^k - 1) equals 6*k.

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

Offset

1,2

Comments

Integers k such that A007953(16^k - 1) = A008588(k). - Iain Fox, Nov 22 2017

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

No other terms below 10^6. - Iain Fox, Nov 25 2017

For all a(n), 2*a(n) is in A294652. - Iain Fox, Dec 02 2017

Links

Table of n, a(n) for n=1..21.

Example

For k=1, 16-1 is 15 with sum of digits 6, so 1 is a term.
For k=2, 16^2-1 is 255 with sum of digits 12, so 2 is a term.

Mathematica

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

Prog

(PARI) is(n) = 6*n == sumdigits(16^n-1) \\ Iain Fox, Nov 24 2017

Crossrefs

Cf. A007953, A294652.

Sequence in context: A165805 A319975 A307625 * A082400 A072993 A018444

Adjacent sequences: A165719 A165720 A165721 * A165723 A165724 A165725

Keyword

base,more,nonn

Author

Max Alekseyev, Sep 24 2009

Status

approved