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 A277225 #50 Oct 18 2021 14:09:33
%S A277225 1,16,97,241,3302449,123402049,2163898897,4168758049,10062413521,
%T A277225 18006326449,21376916449,55487798449,77248867921,108396336049,
%U A277225 141466251697,183357512449,198504183697,200642120449,278584843921,282955076449,341261911249,723039200449,770057874097,847823354449
%N A277225 Initial values of runs of 5 consecutive numbers all of which are squares, primes, or products of one prime and one square.
%C A277225 The existence of runs of 6 or 7 numbers with the same property is an open question; a run of length 8 is impossible. - _Andrey Zabolotskiy_, Nov 07 2016
%C A277225 Numbers n such that each of the five consecutive integers k in n..n+4 has A162642(k)<2. - _Jason Kimberley_, Aug 27 2017
%C A277225 There is no n in this sequence below 10^10000 such that n+1 is also in this sequence. In other words, no n below 10^10000 such that each of the six consecutive integers n..n+5 has squarefree rank less than two. - Roger Eggleton and _Jason Kimberley_, Sep 02 2017
%H A277225 Charles R Greathouse IV, <a href="/A277225/b277225.txt">Table of n, a(n) for n = 1..400</a>
%H A277225 Moscow Mathematical Olympiad, <a href="http://olympiads.mccme.ru/mmo/2015/78mmo.pdf">LXXVIII Moscow Mathematical Olympiad: Problems and Solutions</a>, 2015 (in Russian), Question 4 for Grade 8 by D. M. Krekov (pages 5 and 15-16).
%e A277225 For n=16, the five numbers in the group are 16 (square) 17 (prime) 18 (prime * square) 19 (prime) 20 (prime * square).
%o A277225 (PARI) sp(x)=local(c);c=core(x);isprime(c)||(c==1)
%o A277225 for(n=1, 100000000000, if(vector(5, i, 1)==vector(5, i, sp(n+i-1)), print1(n, ", ")))
%o A277225 (PARI) has(n)=if(isprime(n), return(1)); forprime(p=2,97, if(n%p==0, my(e=valuation(n,p)); if(e%2, return(issquare(n/p)), n/=p^e))); issquare(n) || isprime(core(n))
%o A277225 is(n)=for(k=n,n+4,if(!has(k), return(0))); 1
%o A277225 print1(1); for(s=2,1e7, t=2*s^2; if(!has(t-1) || !has(t+1), next); for(n=t-3,t-1, if(is(n), print1(", "n)))) \\ _Charles R Greathouse IV_, Oct 14 2016
%Y A277225 Cf. A229125, A265640, A290340.
%K A277225 nonn
%O A277225 1,2
%A A277225 _Charles Bowyer_, Oct 14 2016
%E A277225 a(7)-a(24) from _Charles R Greathouse IV_, Oct 14 2016