A252494 Numbers n such that all prime factors of n and n+1 are <= 11. (Related to the abc conjecture.)

1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 14, 15, 20, 21, 24, 27, 32, 35, 44, 48, 49, 54, 55, 63, 80, 98, 99, 120, 125, 175, 224, 242, 384, 440, 539, 2400, 3024, 4374, 9800

Offset: 1

Author

M. F. Hasler, Jan 16 2015

Keywords

• nonn
• fini
• full

Comments

This sequence is complete by a theorem of Stormer, cf. A002071.

This is the 5th row of the table A138180. It has 40=A002071(5)=A145604(1)+...+ A145604(5) terms and ends with A002072(5)=9800. It is the union of all terms in rows 1 through 5 of the table A145605.

This is a subsequence of A252493, and contains A085152 and A085153 as subsequences.

Links

• OEIS Index entries for sequences related to the abc conjecture

Crossrefs

Cf. A002071, A145604, A138180, A145605, A002072, A085152, A085153, A252493, A252492.

Programs

Mathematica

Select[Range[10000], FactorInteger[ # (# + 1)][[ -1,1]] <= 11 &]

PARI

for(n=1,9e6,vecmax(factor(n++)[,1])<12 && vecmax(factor(n--+(n<2))[,1])<12 && print1(n",")) \\ Skips 2 if n+1 is not 11-smooth: Twice as fast as the naive version.