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 A085153 All prime factors of n and n+1 are <= 7. (Related to the abc conjecture.) 30
 1, 2, 3, 4, 5, 6, 7, 8, 9, 14, 15, 20, 24, 27, 35, 48, 49, 63, 80, 125, 224, 2400, 4374 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,2 COMMENTS 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). This sequence is complete by a theorem of Stormer. See A002071. - T. D. Noe, Mar 03 2008 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 Equivalently, this is the sequence of numbers for which A074399(n) <= 7, or A252489(n) <= 4. LINKS Abderrahmane Nitaj, The ABC conjecture homepage MATHEMATICA Select[Range, FactorInteger[ # (# + 1)][[ -1, 1]] <= 7 &] - T. D. Noe, Mar 03 2008 PROG (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 CROSSREFS Cf. A085152, A002473, A086247. Sequence in context: A334918 A125506 A079334 * A339111 A130010 A282765 Adjacent sequences:  A085150 A085151 A085152 * A085154 A085155 A085156 KEYWORD nonn,fini,full AUTHOR Benoit Cloitre, Jun 21 2003 EXTENSIONS Edited by Dean Hickerson, Jun 30 2003 STATUS approved

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Last modified April 13 10:24 EDT 2021. Contains 342935 sequences. (Running on oeis4.)