Numbers n such that 2^(2*n)-1 = 63 (mod 3*(n+2)), 2^(n-1) == 1(mod n) and n == 6 (mod 7)

83, 293, 503, 1553, 2393, 3863, 4283, 4703, 6803, 7433, 7853, 9533, 9743, 11213, 12893, 13103, 13313, 14783, 15413, 16253

in OEIS add A173654

all elements satisfy the condition.

A141570 Primes of the form 2*3*5*7*n+83.

Our sequence is a subsequence for A141570

please help me find a pseudo-prime element of my sequence

ps verified for n<5*10^8

ps2 768440063

topic can be removed