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Numbers n such that all prime factors of n and n+1 are <= 11. (Related to the abc conjecture.)
6

%I #9 Jan 16 2015 09:25:44

%S 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,

%T 98,99,120,125,175,224,242,384,440,539,2400,3024,4374,9800

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

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

%C 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.

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

%H <a href="/index/Ab#abc">OEIS Index entries for sequences related to the abc conjecture</a>

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

%o (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.

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

%K nonn,fini,full

%O 1,2

%A _M. F. Hasler_, Jan 16 2015