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a(n) = smallest number >= a(n-1) such that a(1)*a(2)*...*a(n)+1 is prime; a(1)=2.
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%I #8 Jan 19 2023 03:27:12

%S 2,2,3,3,3,4,5,7,10,14,15,18,30,32,46,56,58,59,84,86,99,101,103,106,

%T 122,126,128,128,136,152,157,170,190,208,281,282,284,320,393,406,459,

%U 479,526,529,530,540,559,601,639,640,709,789,828,900,917,949,1029,1029

%N a(n) = smallest number >= a(n-1) such that a(1)*a(2)*...*a(n)+1 is prime; a(1)=2.

%H Amiram Eldar, <a href="/A173910/b173910.txt">Table of n, a(n) for n = 1..700</a>

%t a[1] = 2; a[n_] := a[n] = Module[{k = a[n - 1], r = Product[a[i], {i, 1, n - 1}]}, While[! PrimeQ[k*r + 1], k++]; k]; Array[a, 60] (* _Amiram Eldar_, Jan 19 2023 *)

%Y Cf. A036012, A046966.

%K nonn

%O 1,1

%A _Dmitry Kamenetsky_, Mar 02 2010

%E More terms from _Amiram Eldar_, Jan 19 2023