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a(n) is the least prime == 2*a(n-2) mod a(n-1); a(1) = 2, a(2) = 3.
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%I #9 Apr 11 2023 02:07:16

%S 2,3,7,13,53,79,659,6089,104831,955657,20278459,103303609,557074963,

%T 1877832107,2991982033,6747646247,12731610313,179006226563,

%U 10944843040969,76971913739909,98861599821847,7568563814118343,492154371117335989,8381761436622948499,177001298911316590457,6919814180414592924821

%N a(n) is the least prime == 2*a(n-2) mod a(n-1); a(1) = 2, a(2) = 3.

%C The sequence of least primes == 2*a(n-1) mod a(n-2), starting with a(1) = 2 and a(2) = 3, is 2, 3, 2, 7, 2, 11, 2, 37, 2, 41, 2, 127, 2, 131, ..., the interleaving of 2 and A362005.

%H Robert Israel, <a href="/A361988/b361988.txt">Table of n, a(n) for n = 1..391</a>

%e a(4) = 13 because 13 is the first prime == 2*3 (mod 7).

%p A[1]:= 2: A[2]:= 3:

%p for i from 3 to 30 do

%p for k from 2*A[i-2] mod A[i-1] by A[i-1] do

%p if isprime(k) then A[i]:= k; break fi

%p od

%p od:

%p seq(A[i],i=1..30);

%Y Cf. A362005.

%K nonn

%O 1,1

%A _Robert Israel_, Apr 02 2023