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

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

1,1

Comments

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.

Links

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

OEIS Index entries for sequences related to the abc conjecture

Mathematica

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

Prog

(PARI) 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.

Crossrefs

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

Sequence in context: A374559 A244431 A151977 * A319281 A022106 A041518

Adjacent sequences: A252489 A252490 A252491 * A252493 A252494 A252495

Keyword

nonn,fini,full

Author

M. F. Hasler, Jan 16 2015

Status

approved