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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

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: A092597 A125506 A079334 * A130010 A282765 A033081

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 January 22 10:25 EST 2020. Contains 331144 sequences. (Running on oeis4.)