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Primes p = prime(i) of level (1,3), i.e., such that A118534(i) = prime(i-3).
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%I #26 Aug 28 2021 18:18:55

%S 619,1069,1459,1499,1759,1789,2861,3331,3931,4177,4801,4831,5419,6229,

%T 6397,8431,8893,9067,9631,11003,11131,11789,12619,14251,15331,15889,

%U 16661,17683,17939,18269,18553,19219,19391,19507,20029,20759,22039,22159,22171,22549

%N Primes p = prime(i) of level (1,3), i.e., such that A118534(i) = prime(i-3).

%C If prime(i) has level 1 in A117563 and 2*prime(i) - prime(i+1) = prime(i-k), then we say that prime(i) has level (1,k).

%H Remi Eismann, <a href="/A118467/b118467.txt">Table of n, a(n) for n = 1..10000</a>

%e prime(115) - prime(114) = 631 - 619 = 619 - 607 = prime(114) - prime(114-3).

%t Select[Partition[Prime[Range[2600]],5,1],#[[5]]-#[[4]]==#[[4]]-#[[1]]&][[All,4]] (* _Harvey P. Dale_, Aug 28 2021 *)

%Y Subsequence of A125830 and A162174.

%Y Cf. A006562 (primes of level (1,1)), A117078, A117563, A117876, A118464.

%K nonn

%O 1,1

%A _RĂ©mi Eismann_, May 24 2006

%E Definition and comment reworded, following author's suggestions, by _M. F. Hasler_, Nov 30 2009