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 A185165 #14 Jun 24 2017 17:23:42 %S A185165 2,6,8,20,42,75,90,117,154,156,189,220,363,385,490,525,702,775,777, %T A185165 845,975,990,1050,1183,1276,1300,1505,1587,1628,1742,1806,1824,1860, %U A185165 1905,1911,2436,2496,2523,2541,2793,2860,2943,3660,3720,3800,3960,4309,5043,5060,5390,5540,5994,6069,6160,6664,6845,8127,8268,8325,8427 %N A185165 Numbers n such that lambda(n) = lambda(n - lambda(n)). %C A185165 Lambda is the function in A002322. If there are infinitely many Sophie Germain primes (conjecture), then this sequence is infinite. Proof: The numbers of the form 3p^2 are in a subsequence if p and 2p+1 are both prime with p > 3, because from the property that lambda(3p^2) = p(p-1) and lambda (p(2p+1)) = p(p-1), if m = 3p^2 then lambda(m-phi(m)) = lambda (3p^2 - p(p-1)) = lambda(p(2p+1)) = p(p-1) = lambda(m). %H A185165 G. C. Greubel, <a href="/A185165/b185165.txt">Table of n, a(n) for n = 1..1000</a> %e A185165 75 is in the sequence because lambda(75) = 20, lambda(75 - 20) = lambda(55) = 20. %t A185165 Select[Range[20000], CarmichaelLambda[ #] == CarmichaelLambda[ # - CarmichaelLambda[#] ] &] %Y A185165 Cf. A002322, A005384. %Y A185165 Cf. A051487 (numbers n such that phi(n) = phi(n - phi(n))). %K A185165 nonn %O A185165 1,1 %A A185165 _Michel Lagneau_, Mar 31 2011