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

Author

Benoit Cloitre, Jun 21 2003

Keywords

• nonn
• fini
• full

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
• OEIS Index entries for sequences related to the abc conjecture

Crossrefs

Cf. A085152, A002473, A086247.

Programs

Mathematica

Select[Range[10000], FactorInteger[ # (# + 1)][[ -1,1]] <= 7 &] (* T. D. Noe, Mar 03 2008 *)

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

Extensions

Edited by Dean Hickerson, Jun 30 2003