A227420 -id:A227420 - cp's OEIS frontend

A061067 m-th prime prime(m) is included iff prime(m) + m is also prime.

2, 3, 7, 13, 61, 79, 89, 101, 131, 139, 181, 223, 317, 349, 359, 421, 479, 503, 521, 541, 557, 569, 577, 593, 619, 641, 701, 733, 827, 863, 881, 929, 1021, 1069, 1223, 1231, 1249, 1277, 1361, 1399, 1439, 1487, 1733, 1831, 1889, 1987, 2069, 2137, 2143, 2203

Offset: 0

Labos Elemer, May 28 2001

nonn

			5th term here is 61 = prime(18) and 61 + 18 = 79.

Harry J. Smith, Table of n, a(n) for n = 0..1000

Cf. A064402, A061068, A227420.

[NthPrime(n): n in [1..250] | IsPrime(NthPrime(n)+ n)]; // Vincenzo Librandi, Jan 19 2015

Prime[Select[Range[500], PrimeQ[Prime[ # ] + # ] &]] (* Stefan Steinerberger, Jul 21 2006 *)
Select[Prime[Range[400]],PrimeQ[#+PrimePi[#]]&] (* Harvey P. Dale, Oct 03 2016 *)

{ n=-1; m=0; forprime (p=2, 109597, if (isprime(p + m++), write("b061067.txt", n++, " ", p)) ) } \\ Harry J. Smith, Jul 17 2009

a(n) + A064402(n+1) = A061068(n+1). [corrected by Martin Fuller]

Edited by N. J. A. Sloane at the suggestion of Andrew S. Plewe, Aug 23 2007

A231326 Primes p such that p - 2*k is also prime, where p is k-th prime.

Original entry on oeis.org

17, 19, 23, 37, 47, 67, 71, 73, 83, 89, 97, 113, 131, 137, 139, 149, 151, 157, 167, 179, 181, 197, 199, 223, 233, 263, 307, 331, 353, 379, 397, 419, 421, 439, 443, 457, 461, 463, 503, 557, 587, 613, 631, 641, 643, 659, 661, 677, 701, 719, 743, 761, 773, 839, 863

Offset: 1

K. D. Bajpai, Nov 07 2013

nonn

			a(2)= 19 which is 8th prime. prime(8)-2*8= 19-16= 3 which is also prime.
a(6)= 67 which is 19th prime. prime(19)-2*19= 67-38= 29 which is also prime.

K. D. Bajpai, Table of n, a(n) for n = 1..5200

Cf. A061068 (primes: prime(m) plus its subscript).
Cf. A064402 (numbers n: prime(n)+n is prime).
Cf. A227420 (primes: p - pi(p) is also prime).
Cf. A231232 (primes: prime(k)+2*k is also prime).

KD := proc() local a,b; a:= ithprime(n); b := a-2*n; if isprime(b) then RETURN (a); fi;end: seq(KD(),n=1..500);

TK = Select[Table[{Prime[n], Prime[n] - 2*n}, {n, 200}], PrimeQ[#[[2]]] &]; Transpose[TK][[1]]

cp's OEIS Frontend

A061067 m-th prime prime(m) is included iff prime(m) + m is also prime.

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