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 A116017 #38 May 28 2025 23:10:05
%S A116017 1,2,3,4,5,9,34,141,198,277,297,375,499,1420,2651,2777,3554,4999,
%T A116017 19050,28660,29128,49999,131061,506311,3844863,3852517,4761903,
%U A116017 4999999,22222218,37560831,133878933,506767303,872011214,1381799253,1427435733,2777777777,3018915632,3555555554
%N A116017 Numbers m such that m + sigma(m) is a repdigit.
%C A116017 From _Farideh Firoozbakht_, Aug 17 2006: (Start)
%C A116017 (1) If p=(10^(3n+2)-19)/27 is a prime greater than 3 then m=6p is in the sequence because m+sigma(m)=6*(10^(3n+2)-1)/9 (the proof is easy), so m+sigma(m) is a repdigit number. The smallest such terms is 22222218, the next such term is 6*(10^(3*430+2)-1)/9=222...218 which has 1292 digits.
%C A116017 (2) If p=5*10^n-1 is prime then p is in the sequence because p+sigma(p)=10^(n+1)-1, so p+sigma(p) is a repdigit number. 499, 49999, 4999999,... are such terms.
%C A116017 (3) If p=(25*10^(n-1)-7)/9 is prime then p is in the sequence because p+sigma(p)=5*(10^n-1)/9, so p+sigma(p) is a repdigit number. 2, 277, 2777, 2777777777, ... are such terms.
%C A116017 (4) If p=(16*10^(n-1)-7)/9 is prime then m=2p is in the sequence because m+sigma(m)=8*(10^n-1) /9, so m+sigma(m) is a repdigit number. 34, 3554, 3555555554, ... are such terms. (End)
%H A116017 Max Alekseyev, <a href="/A116017/b116017.txt">Table of n, a(n) for n = 1..61</a> (terms 1..45 from Hiroaki Yamanouchi, terms 46..51 from Giovanni Resta)
%e A116017 22222218 + sigma(22222218) = 66666666.
%t A116017 Do[If[Length[Union[IntegerDigits[n + DivisorSigma[1, n]]]]==1, Print[n]], {n, 60000000}] (* _Farideh Firoozbakht_, Aug 17 2006 *)
%o A116017 (PARI)
%o A116017 for(n=1, 10^7, d=digits(sigma(n)+n); c=0; for(i=1, #d-1, if(d[i]!=d[i+1], c++; break)); if(c==0, print1(n, ", "))) \\ _Derek Orr_, Aug 01 2014
%o A116017 (Python)
%o A116017 from sympy import divisors
%o A116017 A116017 = [n for n in range(1,10**5) if len(set(str(n+sum(divisors(n))))) == 1] # _Chai Wah Wu_, Aug 11 2014
%Y A116017 Contains A244444 as subsequence.
%Y A116017 Cf. A116018, A096841.
%K A116017 nonn,base
%O A116017 1,2
%A A116017 _Giovanni Resta_, Feb 13 2006
%E A116017 More terms from _Farideh Firoozbakht_, Aug 17 2006, Dec 19 2007
%E A116017 a(36)-a(37) from _Donovan Johnson_, Feb 17 2013
%E A116017 a(38) from _Farideh Firoozbakht_, Aug 01 2014