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 A085153 #21 Aug 09 2025 17:23:04
%S A085153 1,2,3,4,5,6,7,8,9,14,15,20,24,27,35,48,49,63,80,125,224,2400,4374
%N A085153 All prime factors of n and n+1 are <= 7. (Related to the abc conjecture.)
%C A085153 The ABC conjecture would imply that if the prime factors of A, B, C are prescribed in advance, then there is only a finite number of solutions to the equation A + B = C with gcd(A,B,C)=1 (indeed it would bound C to be no more than "roughly" the product of those primes). So in particular there ought to be only finitely many pairs of adjacent integers whose prime factors are limited to {2, 3, 5, 7} (D. Rusin).
%C A085153 This sequence is complete by a theorem of Stormer. See A002071. - _T. D. Noe_, Mar 03 2008
%C A085153 This is the 4th row of the table A138180. It has 23=A002071(4)=A145604(1)+...+ A145604(4) terms and ends with A002072(4)=4374. It is the union of all terms in rows 1 through 4 of the table A145605. It is a subsequence of A252494 and contains A085152 as a subsequence. - _M. F. Hasler_, Jan 16 2015
%C A085153 Equivalently, this is the sequence of numbers for which A074399(n) <= 7, or A252489(n) <= 4.
%H A085153 Abderrahmane Nitaj, <a href="https://nitaj.users.lmno.cnrs.fr/abc.html">The ABC conjecture homepage</a>
%H A085153 <a href="/index/Ab#abc">OEIS Index entries for sequences related to the abc conjecture</a>
%t A085153 Select[Range[10000], FactorInteger[ # (# + 1)][[ -1,1]] <= 7 &] (* _T. D. Noe_, Mar 03 2008 *)
%o A085153 (PARI) for(n=1,9e6,vecmax(factor(n++)[,1])<8 && vecmax(factor(n--+(n<2))[,1])<8 && print1(n",")) \\ _M. F. Hasler_, Jan 16 2015
%Y A085153 Cf. A085152, A002473, A086247.
%K A085153 nonn,fini,full
%O A085153 1,2
%A A085153 _Benoit Cloitre_, Jun 21 2003
%E A085153 Edited by _Dean Hickerson_, Jun 30 2003