A086247 -id:A086247 - cp's OEIS frontend

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

Benoit Cloitre, Jun 21 2003

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.

Abderrahmane Nitaj, The ABC conjecture homepage
OEIS Index entries for sequences related to the abc conjecture

Cf. A085152, A002473, A086247.

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

for(n=1,9e6,vecmax(factor(n++)[,1])<8 && vecmax(factor(n--+(n<2))[,1])<8 && print1(n",")) \\ M. F. Hasler, Jan 16 2015

Edited by Dean Hickerson, Jun 30 2003

A252492 The largest prime factor of n*(n+1) equals 17. (Related to the abc conjecture.)

Original entry on oeis.org

16, 17, 33, 34, 50, 51, 84, 119, 135, 153, 169, 220, 255, 272, 288, 374, 441, 560, 594, 714, 832, 935, 1088, 1155, 1224, 1274, 1700, 2057, 2430, 2499, 2600, 4913, 5831, 12375, 14399, 28560, 31212, 37179, 194480, 336140

Offset: 1

M. F. Hasler, Jan 16 2015

Equivalently, the prime factors of n and n+1 are not larger than 17, but not all smaller than 17 (in which case n is in A252493).
This sequence is complete by a theorem of Stormer, cf. A002071 and sequences A085152, A085153, A252494, A252493.
This is row 7 of A145605. It has A145604(7)=40 terms and ends with A002072(7)=336140.

OEIS Index entries for sequences related to the abc conjecture

Cf. A002473, A086247, A252493, A252494, A085153, A085152.

Select[Range[345678], FactorInteger[ # (# + 1)][[ -1,1]] == 17 &]

for(n=1,9e6,vecmax(factor(n++)[,1])<18 && vecmax(factor(n*n--)[,1])==17 && print1(n",")) \\ Skips 2 if n+1 is not 17-smooth: Twice as fast as the naïve version.

cp's OEIS Frontend

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

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