A014692 -id:A014692 - cp's OEIS frontend

A234852 Indices k of primes p=prime(k) such that prime(p)-p+1 is prime.

1, 2, 3, 4, 6, 7, 9, 11, 13, 14, 18, 20, 23, 24, 27, 29, 34, 36, 40, 42, 46, 47, 48, 53, 58, 59, 60, 62, 63, 64, 66, 68, 70, 71, 73, 90, 95, 100, 103, 105, 110, 121, 122, 127, 128, 132, 133, 134, 141, 143, 144, 153, 155, 156, 162

Offset: 1

M. F. Hasler, Dec 31 2013

nonn

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

Select[Range[200],PrimeQ[Prime[Prime[#]]-Prime[#]+1]&] (* Harvey P. Dale, Jul 14 2024 *)

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

a(n) = PrimePi(A234695(n)), PrimePi = A000720.

A107819 Slowest increasing sequence where a(n)+n is prime.

Original entry on oeis.org

1, 3, 4, 7, 8, 11, 12, 15, 20, 21, 26, 29, 30, 33, 38, 43, 44, 49, 52, 53, 58, 61, 66, 73, 76, 77, 80, 81, 84, 97, 100, 105, 106, 115, 116, 121, 126, 129, 134, 139, 140, 149, 150, 153, 154, 165, 176, 179, 180, 183

Offset: 1

Eric Angelini, Jun 11 2005

Appears to be closely related to A014692.

			(1)+1=2, which is prime; (3)+2=5=prime; (4)+3=7=prime; (7)+4=11=prime; (8)+5=13=prime; etc.

A107819 := proc(n)
        option remember;
        if n = 1 then
                return 1;
        else
                for a from procname(n-1)+1 do
                        if isprime(a+n) then
                                return a;
                        end if;
                end do:
        end if;
end proc: # R. J. Mathar, Sep 05 2011

@cached_function
def A107819(n):
    prev = (-1 if n == 1 else A107819(n-1))
    return next_prime(prev+n)-n  # D. S. McNeil, Sep 05 2011

Corrected by R. J. Mathar, Sep 05 2011

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

A234852 Indices k of primes p=prime(k) such that prime(p)-p+1 is prime.

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A107819 Slowest increasing sequence where a(n)+n is prime.

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Maple

Sage

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A234853 Indices of primes in A234851.

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PARI