This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.
%I A225539 #32 Dec 29 2018 15:54:45
%S A225539 5,16,23,34,41,52,59,70,77,88,95,106,113,124,131,142,149,160,167,178,
%T A225539 185,196,203,214,221,232,239,250,257,268,275,286,293,304,311,322,329,
%U A225539 340,347,358,365,376,383,394,401,412,419,430,437,448
%N A225539 Numbers n where 2^n and n have the same digital root.
%C A225539 The digital roots of n have a cycle length of 9 (A010888) and the digital roots of 2^n have a cycle length of 6 (A153130). Therefore, if n is a term so is n+18.
%C A225539 The only values of the digital roots of a(n) are 5 and 7 (A010718).
%H A225539 <a href="/index/Rec#order_03">Index entries for linear recurrences with constant coefficients</a>, signature (1,1,-1).
%F A225539 a(n) = 9*n - 3 + (-1)^n.
%F A225539 a(n) = a(n-1) + 7 (odd n), a(n) = a(n-1) + 11 (even n) with a(1) = 5.
%F A225539 G.f. x*(5 + 11*x + 2*x^2) / ((1-x)^2 * (1+x)). - _Joerg Arndt_, May 17 2013
%e A225539 For n=23, the digital root of n is 5. 2^n equals 8388608 so the digital root of 2^n is 5 as well.
%t A225539 digitalRoot[n_] := Module[{r = n}, While[r > 9, r = Total[IntegerDigits[ r]]]; r]; Select[Range[448], digitalRoot[2^#] == digitalRoot[#] &] (* _T. D. Noe_, May 19 2013 *)
%t A225539 LinearRecurrence[{1,1,-1},{5,16,23},60] (* _Harvey P. Dale_, Dec 29 2018 *)
%o A225539 (PARI) forstep(n=16,500,[7,11],print1(n", ")) \\ _Charles R Greathouse IV_, May 19 2013
%Y A225539 Cf. A010888, A153130, A010718.
%K A225539 nonn,base,easy
%O A225539 1,1
%A A225539 _Marcus Hedbring_, May 17 2013