A234852 -id:A234852 - cp's OEIS frontend

A234695 Primes p with prime(p) - p + 1 also prime.

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

Offset: 1

Zhi-Wei Sun, Dec 29 2013

nonn

By the conjecture in A234694, this sequence should have infinitely many terms.

			a(1) = 2 since prime(2) - 1 = 2 is prime.
a(2) = 3 since prime(3) - 2 = 3 is prime.
a(3) = 5 since prime(5) - 4 = 7 is prime.
a(4) = 7 since prime(7) - 6 = 11 is prime.

Zhi-Wei Sun, Table of n, a(n) for n = 1..10000
Z.-W. Sun, Problems on combinatorial properties of primes, arXiv:1402.6641, 2014

Cf. A000040, A014692, A234694.

n=0;Do[If[PrimeQ[Prime[Prime[k]]-Prime[k]+1],n=n+1;Print[n," ",Prime[k]]],{k,1,1000}]

forprime(p=1,999,isprime(prime(p)-p+1)&&print1(p",")) \\ - M. F. Hasler, Dec 31 2013

a(n) = prime(A234852(n)). - M. F. Hasler, Dec 31 2013

A234851 Indices of primes in A014692, i.e., numbers k such that prime(k)-k+1 is prime.

Original entry on oeis.org

1, 2, 3, 5, 7, 13, 17, 21, 23, 25, 31, 41, 43, 49, 61, 71, 77, 83, 89, 103, 105, 109, 121, 129, 133, 139, 151, 161, 173, 181, 183, 185, 189, 199, 211, 213, 223, 231, 235, 241, 243, 247, 265, 271, 273, 277, 279, 281, 285, 293, 301, 303, 307, 311, 317

Offset: 1

M. F. Hasler, Dec 31 2013

nonn

Sequence A234695 lists primes in this sequence.

Robert Israel, Table of n, a(n) for n = 1..10000

Cf. A000040, A000720, A014692, A234695, A234850, A234852.

select(k -> isprime(ithprime(k)-k+1), [$1..1000]); # Robert Israel, Feb 19 2021

for(k=1,999,isprime(prime(k)-k+1)&&print1(k","))

PARI
```
is_A234851(n)=isprime(prime(k)-k+1)
```

a(n) = PrimePi(A234850(n)), PrimePi = A000720.

A234853 Indices of primes in A234851.

Original entry on oeis.org

2, 3, 4, 5, 6, 7, 9, 11, 12, 13, 15, 16, 18, 19, 20, 22, 26, 27, 29, 30, 34, 35, 37, 40, 44, 46, 48, 50, 53, 54, 55, 59, 60, 61, 62, 68, 76, 79, 80, 81, 85, 89, 91, 94, 96, 99, 100, 102, 110, 111, 112, 117, 122, 123, 125, 126, 134, 138, 139, 141, 144, 147

Offset: 1

M. F. Hasler, Dec 31 2013

nonn

Cf. A000040, A000720, A014692, A234850, A234851, A234852, A234695.

c=0;for(k=1,1999,isprime(prime(k)-k+1)&&c++&&isprime(k)&&print1(c", "))

cp's OEIS Frontend

A234695 Primes p with prime(p) - p + 1 also prime.

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A234851 Indices of primes in A014692, i.e., numbers k such that prime(k)-k+1 is prime.

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A234853 Indices of primes in A234851.

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PARI