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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

%I

%S 1,2,2,3,6,46,1306,7695,17383720,2183805400,60512359083,447808566362,

%T 181830203704703

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

%C a(14) > 2.5*10^14, if it exists. - _Don Reble_, Nov 22 2015

%C 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

%C 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 non-monotonic 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

%e 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.

%o (PARI) A096100(n, show=0, a=[1])={for(n=1, n-1, show&&print1(a[n]", "); for(k=2, 9e9, my(p=1); for(i=0,n-1,isprime(1+k*p*=a[n-i])||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

%K more,nonn

%O 1,2

%A _Amarnath Murthy_, Jun 24 2004

%E Edited, corrected and extended by _Klaus Brockhaus_, Jul 05 2004

%E a(10) from _Donovan Johnson_, Apr 22 2008

%E a(11)-a(13) from _Don Reble_, Nov 22 2015

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Last modified October 15 19:25 EDT 2019. Contains 328037 sequences. (Running on oeis4.)