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 A075029 #36 May 30 2025 17:27:51
%S A075029 1,4,45,80,28974,28974,8489103,80314575,5196065775,77506573550,
%T A075029 166622964149389,489289301397948
%N A075029 a(n) is the smallest number k such that the number of divisors of the n numbers from k through k+n-1 are decreasing.
%C A075029 a(11) > 10^12. - _Donovan Johnson_, Oct 13 2009
%C A075029 a(11) > 10^13. - _Giovanni Resta_, Jul 25 2013
%C A075029 a(13) > 2.64*10^15. - _Jud McCranie_, Mar 27 2019
%D A075029 J.-M. De Koninck, Ces nombres qui nous fascinent, Entry 45, p. 17, Ellipses, Paris 2008.
%e A075029 a(4) = 80, as tau(80) = 10 > tau(81) = 5 > tau(82) = 4 > tau(83) = 2, and no smaller sequence of 4 consecutive integers satisfies such a chain of inequalities.
%o A075029 (PARI) n=2; for(k=1, 100, while(1, m=n; s=1; while(numdiv(m)<numdiv(m-1), s=s+1; m=m+1); if(s>=k, print1(n-1, ", "); break); n=n+1))
%o A075029 (PARI) apply( {A075029(n)=for(k=4^(n-1),oo, my(d=numdiv(k)); d<n && next; for(j=1,n-1, d>(d=numdiv(k+j)) || [k+=j-1, next(2)]); return(k))}, [1..6]) \\ For illustration - becomes slow for n >= 7. - _M. F. Hasler_, May 26 2025
%Y A075029 Cf. A075028, A075031.
%Y A075029 Cf. A000005 (numdiv).
%K A075029 nonn,more
%O A075029 1,2
%A A075029 _Amarnath Murthy_, Sep 02 2002
%E A075029 Edited by _Ralf Stephan_, Mar 21 2003
%E A075029 Definition corrected by _Leroy Quet_, Feb 23 2008
%E A075029 2 more terms from _Lekraj Beedassy_, Jul 13 2008
%E A075029 a(9)-a(10) from _Donovan Johnson_, Oct 13 2009
%E A075029 a(11)-a(12) from _Jud McCranie_, Mar 27 2019
%E A075029 Definition changed by _Robert Israel_, May 26 2025