OFFSET
1,1
COMMENTS
Conjecture: this sequence contains no terms k where k+1 is prime. (All similar sequences that start with numbers less than 252 are known to contain terms k where k+1 is prime.)
The next few similar sequences that seem to have this property are those that begin with a(1) = 322, 622, 664, 776, and 830. - J. Lowell, Mar 25 2014
Adding 1 to the 30th term of this sequence gives a 152-digit composite number with no factors found in ECM after hundreds of curves. - J. Lowell, Jan 11 2022
The above conjecture has now been disproved: adding 1 to the 39th term of this sequence gives a prime number. - Andrea Concaro, Dec 31 2022
Calculating a(114) requires partial factorization of a(113)+1, a 1022-digit composite number. - Tyler Busby, Jan 21 2023
LINKS
Tyler Busby, Table of n, a(n) for n = 1..43 (terms 1..30 from Jon E. Schoenfield, terms 31..39 from Andrea Concaro)
Tyler Busby, Conjectured Table of n, a(n) for n = 1..113 using elliptic-curve factorization to obtain probable smallest factors when other methods were computationally unfeasible.
factordb, Status of a(113)+1.
FORMULA
Conjecture: a(n) = A238642(a(n-1)). - J. Lowell, Mar 25 2014 [This conjecture fails at n=40; see the above comment from Andrea Concaro. - Jon E. Schoenfield, Jan 15 2023]
EXAMPLE
First term is 252. Smallest prime factor of 253 is 11, so next term is 252 * 11 = 2772.
MATHEMATICA
a = {252}; Do[AppendTo[a, a[[ -1]]*FactorInteger[a[[ -1]] + 1][[1, 1]]], {10}]; a (* Stefan Steinerberger, Dec 06 2008 *)
NestList[#*FactorInteger[#+1][[1, 1]]&, 252, 20] (* Harvey P. Dale, Apr 03 2015 *)
PROG
(PARI) findsmallestfactor(n)=if(isprime(n), n, forprime(p=2, 1e6, if(n%p==0, return(p))); factor(n)[1, 1])
lista(n)={vals=Vec([252], n); for(i=2, n, vals[i]=findsmallestfactor(vals[i-1]+1)*vals[i-1]); vals} \\ Tyler Busby, Jan 14 2023
CROSSREFS
KEYWORD
nonn
AUTHOR
J. Lowell, Dec 05 2008
EXTENSIONS
More terms from Stefan Steinerberger, Dec 06 2008
Extended by Max Alekseyev, Sep 19 2009
STATUS
approved