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 A075127 #17 Oct 30 2015 16:51:45 %S A075127 9,243,289,9801,332929,11309769,384199201,13051463049,443365544449, %T A075127 15061377048201,511643454094369,17380816062160329,590436102659356801, %U A075127 20057446674355970889,681362750825443653409 %N A075127 Safe perfect powers: perfect powers n such that (n-1)/2 is also a perfect power. %C A075127 If both powers are squares, the smaller square is a triangular number, and all square triangular numbers (A001110) correspond to a member in this sequence. This proves that this sequence is infinite. Are there only finitely many other members, i.e., is A075127 \ A055792 finite? - _Charles R Greathouse IV_, Dec 12 2010 %F A075127 Conjectures from _Colin Barker_, Oct 28 2015: (Start) %F A075127 a(n) = 35*a(n-1)-35*a(n-2)+a(n-3) for n>5. %F A075127 G.f.: x*(234*x^4-8182*x^3+7901*x^2+72*x-9) / ((x-1)*(x^2-34*x+1)). %F A075127 (End) %t A075127 pp = Select[ Range[10^8], Apply[ GCD, Last[ Transpose[ FactorInteger[ # ]]]] > 1 & ]; Select[pp, Apply[GCD, Last[ Transpose[ FactorInteger[( # - 1)/2]]]] > 1 & ] %o A075127 (PARI) for(n=1, 1e10, if(ispower(n) && ispower((n-1)/2), print1(n, ", "))) \\ _Altug Alkan_, Oct 28 2015 %Y A075127 Cf. A001110, A001597, A055792, A070428, A075114. %K A075127 nonn %O A075127 1,1 %A A075127 _Zak Seidov_, Oct 11 2002 %E A075127 One more term from _Robert G. Wilson v_, Oct 16 2002 %E A075127 a(7)-a(15) from _Donovan Johnson_, Mar 10 2010