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2*a(n) are the lengths of record prime gaps immediately following twin primes.

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`%I #9 Mar 02 2020 00:51:21
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`%S 2,3,5,6,9,12,14,15,17,21,26,27,29,30,35,41,45,50,59,60,63,71,74,75,
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`%T 84,92,96,98,104,110,125,129,144,155,156,165,180,201,204,207
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`%N 2*a(n) are the lengths of record prime gaps immediately following twin primes.
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`%C The corresponding locations are provided in A329160, starting at the initial pair 5, 7.
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`%e a(1) = 2 because the prime gap after 5, 7 has length 11 - 7 = 2*a(1) = 4,
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`%e a(2) = 3 because the prime gap after 29,31 has length 37 - 31 = 2*a(2) = 6, with location given by 6*A329160(2) = 30 +- 1. The gaps before all have length 4 (11,13 -> 17), (17,19 -> 23).
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`%o (PARI) p1=5; p2=7; r=0; forprime(p3=11, 1e9, if(p2-p1==2, d=p3-p2; if(d>r, r=d; print1(d/2, ", "))); p1=p2; p2=p3)
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`%Y Cf. A329158, A329159, A329160, A329164, A329165.
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`%K nonn,more
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`%O 1,1
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`%A _Hugo Pfoertner_, Nov 08 2019
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`%E a(39)-a(40) from _Jinyuan Wang_, Mar 01 2020
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