

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

Table of n, a(n) for n=1..13.


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

Sequence in context: A318039 A060631 A275487 * A260161 A195694 A021451
Adjacent sequences: A096097 A096098 A096099 * A096101 A096102 A096103


KEYWORD

more,nonn


AUTHOR

Amarnath Murthy, Jun 24 2004


EXTENSIONS

Edited, corrected and extended by Klaus Brockhaus, Jul 05 2004
a(10) from Donovan Johnson, Apr 22 2008
a(11)a(13) from Don Reble, Nov 22 2015


STATUS

approved



