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 A061513 #9 Jun 24 2016 12:50:35
%S A061513 0,2,4,6,8,10,32,54,76,98,1110,3332,5554,7776,9998,11111110,33333332,
%T A061513 55555554,77777776,99999998,1111111111111110,3333333333333332,
%U A061513 5555555555555554,7777777777777776,9999999999999998,11111111111111111111111111111110,33333333333333333333333333333332
%N A061513 a(0) = 0; a(n) is obtained by incrementing each digit of a(n-1) by 2.
%C A061513 In A061511-A061522, A061746-A061750 when the incremented digit exceeds 9 it is written as a 2-digit string. So 9+1 becomes the 2-digit string 10, etc.
%C A061513 Every term > 8 is made up of only two different consecutive digits, the smaller of which occurs only as the least significant digit.
%C A061513 Otherwise said, these are one less than the odd repdigits (A010785) of length 2^k, cf. formula. - _M. F. Hasler_, Jun 24 2016
%F A061513 a(n) = A061512(n)-1 = (10^2^floor(n/5)-1)/9*(n%5*2+1) - 1, where n%5 means the remainder (in {0..4}) of n divided by 5. - _M. F. Hasler_, Jun 24 2016
%e A061513 Following 32; 3+2 = 5 and 2+2 = 4, hence the next term is 54.
%t A061513 NestList[FromDigits[Flatten[IntegerDigits/@(IntegerDigits[#]+2)]]&,0,30] (* _Harvey P. Dale_, Jul 07 2012 *)
%o A061513 (PARI) A061513(n)=10^2^(n\5)\9*(n%5*2+1)-1 \\ _M. F. Hasler_, Jun 24 2016
%Y A061513 Cf. A061511 - A061522, A061746 - A061750; A061581 - A061587.
%K A061513 base,nonn
%O A061513 0,2
%A A061513 _Amarnath Murthy_, May 08 2001
%E A061513 More terms from Larry Reeves (larryr(AT)acm.org), May 11 2001