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

1,2

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

Table of n, a(n) for n=1..40.

OEIS Index entries for sequences related to the abc conjecture

Mathematica

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

Prog

(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.

Crossrefs

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

Sequence in context: A191923 A191922 A230776 * A030294 A125668 A365472

Adjacent sequences: A252491 A252492 A252493 * A252495 A252496 A252497

Keyword

nonn,fini,full

Author

M. F. Hasler, Jan 16 2015

Status

approved