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

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

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

Table of n, a(n) for n=1..23.

Abderrahmane Nitaj, The ABC conjecture homepage

OEIS Index entries for sequences related to the abc conjecture

Mathematica

Select[Range[10000], 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: A354220 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