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Let prime(i) = i-th prime, let twin(n) = (P,Q) be n-th pair of twin primes; sequence gives prime(P).
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%I #17 Feb 14 2025 03:42:04

%S 5,11,31,59,109,179,277,353,547,587,773,859,1063,1153,1201,1433,1499,

%T 1723,1823,2063,2341,2897,3001,3259,3733,4133,4397,4549,4759,4933,

%U 6217,6311,6353,6653,6841,8101,8221,8377,8513,8747,9293,9973,10433,10559

%N Let prime(i) = i-th prime, let twin(n) = (P,Q) be n-th pair of twin primes; sequence gives prime(P).

%H Amiram Eldar, <a href="/A057470/b057470.txt">Table of n, a(n) for n = 1..10000</a> (terms 1..1000 from Harvey P. Dale)

%F From _Amiram Eldar_, Feb 14 2025: (Start)

%F a(n) = prime(A001359(n)).

%F a(n) = A151799(A151799(A057473(n))). (End)

%e The 3rd pair of twin primes is twin(3) = (11,13), so a(3) = prime(11) = 31.

%t Prime/@Select[Partition[Prime[Range[300]],2,1],#[[2]]-#[[1]]==2&][[;;,1]] (* _Harvey P. Dale_, May 21 2023 *)

%Y Cf. A001359, A057473, A151799.

%K nonn,changed

%O 1,1

%A _Cino Hilliard_, Sep 10 2000

%E More terms from _James A. Sellers_, Sep 11 2000