

A096100


a(1) = 1; for n > 1: a(n) = smallest number >1 such that product of any two or more successive terms + 1 is prime.


5



1, 2, 2, 3, 6, 46, 1306, 7695, 17383720, 2183805400, 60512359083, 447808566362, 181830203704703
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OFFSET

1,2


COMMENTS

a(14) > 2.5*10^14, if it exists.  Don Reble, Nov 22 2015
So far, up through a(13), the sequence is nondecreasing. I don't know a good reason why it should stay that way. (But since candidates for each successive value get rarer, the least candidate will tend to increase.)  Don Reble, Nov 22 2015
I don't think it will be easy to prove that this sequence is nondecreasing. The analogous sequence with other starting values often leads to nonmonotonic sequences, e.g., (3, 2, 2, 3, 26, 876, 15136, ...), (4, 3, 6, 6, 5, 14, 3597, 1218704, ...), or (5, 2, 3, 2, 3, 1176, 40, 142863, ...).  M. F. Hasler, Nov 24 2015


LINKS



EXAMPLE

a(4) is not 2 since 2*2*2 + 1 = 9 is composite, but 2*3 + 1 = 7, 2*2*3 + 1 = 13, 1*2*2*3 + 1 = 13 are all prime, hence a(4) = 3.


PROG

(PARI) A096100(n, show=0, a=[1])={for(n=1, n1, show&&print1(a[n]", "); for(k=2, 9e9, my(p=1); for(i=0, n1, isprime(1+k*p*=a[ni])next(2)); a=concat(a, k); break)); a[n]} \\ Use 2nd or 3rd optional arg to print intermediate terms or to use other starting value(s) of the sequence. Not efficient enough to go beyond a(8).  M. F. Hasler, Nov 24 2015


CROSSREFS



KEYWORD

more,nonn


AUTHOR



EXTENSIONS



STATUS

approved



