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URL: https://oeis.org/A165722

⇱ A165722 - OEIS

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A165722
Positive integers k such that the sum of decimal digits of (16^k - 1) equals 6*k.
2
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
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
Sequence in context: A165805 A319975 A307625 * A382811 A383043 A082400
KEYWORD
base,more,nonn
AUTHOR
Max Alekseyev, Sep 24 2009
STATUS
approved