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 A085152 #23 Jul 13 2025 19:04:59
%S A085152 1,2,3,4,5,8,9,15,24,80
%N A085152 All prime factors of n and n+1 are <= 5. (Related to the abc conjecture.)
%C A085152 Equivalently: Numbers n such that n(n+1) is 5-smooth.
%C A085152 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} (D. Rusin).
%C A085152 This sequence is complete by a theorem of Stormer. See A002071. - _T. D. Noe_, Mar 03 2008
%C A085152 This is the 3rd row of the table A138180. It has 10 = A002071(3) = A145604(1)+A145604(2)+A145604(3) terms and ends with A002072(3) = 80. It is the union of all terms in rows 1 through 3 of the table A145605. It is a subsequence of A252494 and A085153. - _M. F. Hasler_, Jan 16 2015
%H A085152 <a href="/index/Ab#abc">OEIS Index entries for sequences related to the abc conjecture</a>
%t A085152 Select[Range[10000], FactorInteger[ # (# + 1)][[ -1,1]] <= 5 &] (* _T. D. Noe_, Mar 03 2008 *)
%o A085152 (PARI) for(n=1,99,vecmax(factor(n++)[,1])<6 && vecmax(factor(n--+(n<2))[,1])<6 && print1(n", ")) \\ This skips 2 if n+1 is not 5-smooth: twice as fast as the naive version. - _M. F. Hasler_, Jan 16 2015
%Y A085152 Cf. A002071, A145604, A138180, A145605, A002072, A085153, A252493, A252492.
%K A085152 nonn,fini,full
%O A085152 1,2
%A A085152 _Benoit Cloitre_, Jun 21 2003
%E A085152 Edited by _Dean Hickerson_, Jun 30 2003