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Z.-W. Sun, <a href="http://arxiv.org/abs/1402.6641">Problems on combinatorial properties of primes</a>, arXiv:1402.6641, 2014
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a(n) = prime(A234852(n)). - M. F. Hasler, Dec 31 2013
(PARI) forprime(p=1, 999, isprime(prime(p)-p+1)&&print1(p", ")) \\ - M. F. Hasler, Dec 31 2013
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2, 3, 5, 7, 13, 17, 23, 31, 41, 43, 61, 71, 83, 89, 103, 109, 139, 151, 173, 181, 199, 211, 223, 241, 271, 277, 281, 293, 307, 311, 317, 337, 349, 353, 367, 463, 499, 541, 563, 571, 601, 661, 673, 709, 719, 743, 751, 757, 811, 823, 827, 883, 907, 911, 953, 971, 1093, 1117, 1123, 1153
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Primes p with prime(p) - p + 1 also prime.
By the conjecture in A234694, this sequence should have infinitely many terms.
Zhi-Wei Sun, <a href="/A234695/b234695.txt">Table of n, a(n) for n = 1..10000</a>
a(1) = 2 since prime(2) - 1 = 2 is prime.
n=0; Do[If[PrimeQ[Prime[Prime[k]]-Prime[k]+1], n=n+1; Print[n, " ", Prime[k]]], {k, 1, 1000}]