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 A085153 All prime factors of n and n+1 are <= 7. (Related to the abc conjecture.) 30

%I

%S 1,2,3,4,5,6,7,8,9,14,15,20,24,27,35,48,49,63,80,125,224,2400,4374

%N All prime factors of n and n+1 are <= 7. (Related to the abc conjecture.)

%C 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 This sequence is complete by a theorem of Stormer. See A002071. - _T. D. Noe_, Mar 03 2008

%C 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 Equivalently, this is the sequence of numbers for which A074399(n) <= 7, or A252489(n) <= 4.

%H Abderrahmane Nitaj, <a href="https://nitaj.users.lmno.cnrs.fr/abc.html">The ABC conjecture homepage</a>

%H <a href="/index/Ab#abc">OEIS Index entries for sequences related to the abc conjecture</a>

%t Select[Range[10000], FactorInteger[ # (# + 1)][[ -1,1]] <= 7 &] - _T. D. Noe_, Mar 03 2008

%o (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 Cf. A085152, A002473, A086247.

%K nonn,fini,full

%O 1,2

%A _Benoit Cloitre_, Jun 21 2003

%E Edited by _Dean Hickerson_, Jun 30 2003

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Last modified February 19 19:06 EST 2020. Contains 332047 sequences. (Running on oeis4.)