A085152 All prime factors of n and n+1 are <= 5. (Related to the abc conjecture.)

1, 2, 3, 4, 5, 8, 9, 15, 24, 80

Offset

1,2

Comments

Equivalently: Numbers n such that n(n+1) is 5-smooth.

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} (D. Rusin).

This sequence is complete by a theorem of Stormer. See A002071. - T. D. Noe, Mar 03 2008

This is the 3rd row of the table A138180. It has 10 = A002071(3) = A145604(1)+A145604(2)+A145604(3) terms and ends with A002072(3) = 80. It is the union of all terms in rows 1 through 3 of the table A145605. It is a subsequence of A252494 and A085153. - M. F. Hasler, Jan 16 2015

Links

Table of n, a(n) for n=1..10.

OEIS Index entries for sequences related to the abc conjecture

Mathematica

Select[Range[10000], FactorInteger[ # (# + 1)][[ -1, 1]] <= 5 &] (* T. D. Noe, Mar 03 2008 *)

Prog

(PARI) for(n=1, 99, vecmax(factor(n++)[, 1])<6 && vecmax(factor(n--+(n<2))[, 1])<6 && print1(n", ")) \\ This skips 2 if n+1 is not 5-smooth: twice as fast as the naive version. - M. F. Hasler, Jan 16 2015

Crossrefs

Cf. A002071, A145604, A138180, A145605, A002072, A085153, A252493, A252492.

Sequence in context: A054168 A301464 A354829 * A264886 A369294 A287117

Adjacent sequences: A085149 A085150 A085151 * A085153 A085154 A085155

Keyword

nonn,fini,full

Author

Benoit Cloitre, Jun 21 2003

Extensions

Edited by Dean Hickerson, Jun 30 2003

Status

approved