|
%I #34 Dec 30 2023 21:51:36
%S 1,2,3,4,6,7,8,10,12,13,14,20,23,24,25,26,27,28,34,36,41,46,65,71,74,
%T 83,86,89,92,111,120,235,238,253,297,366,446
%N Positive integers k such that the sum of decimal digits of (4^k - 1) equals 3*k.
%C Integers k such that A007953(4^k - 1) = A008585(k).
%C No other terms below 10^6.
%C Conjecture: For k > 446, digsum(4^k - 1) < 3*k. This would mean that no further terms exist in the sequence.
%C If a(n) is even, then a(n)/2 is in A165722.
%e 4^2 - 1 is 15 with sum of digits 6, so 2 is a term.
%e 4^3 - 1 is 63 with sum of digits 9, so 3 is a term.
%e 4^5 - 1 is 1023 with sum of digits 6, so 5 is not a term.
%t Select[Range[2500], 3# == Total[IntegerDigits[4^# - 1]] &] (* _G. C. Greubel_, Nov 28 2017 *)
%o (PARI) is(n) = 3*n == sumdigits(4^n-1)
%Y Cf. A007953, A008585, A165722.
%K nonn,base,more
%O 1,2
%A _Iain Fox_, Nov 27 2017
|
