A318751 Prime-indexed primes q such that prime(q)-q-1 is a prime indexed prime.

5, 17, 353, 859, 4787, 5441, 6353, 6841, 7883, 12503, 13037, 16061, 18617, 20959, 25357, 29137, 33029, 38351, 39199, 44729, 46237, 69491, 80429, 82217, 85597, 89989, 92779, 97001, 107903, 129287, 132611, 139661, 170707, 172721, 187123, 230453, 238943, 242129, 257689, 259151, 292841, 312773, 328789, 341423, 346147

Offset

1,1

Comments

This sequence and the sequence of resulting primes, prime(q)-q-1 (5, 41, 2027, 5801, 41491, ...), are subsequences of A006450, the prime-indexed primes.

Links

Harvey P. Dale, Table of n, a(n) for n = 1..500

N. Fernandez, An order of primeness, F(p)

N. Fernandez, An order of primeness [cached copy, included with permission of the author]

Maple

N := 1000000;
for n to N do
if isprime(n) then q := ithprime(n);
Z := numtheory[pi](n);
S := q-n-1;
W := numtheory[pi](S);
if isprime(Z) and isprime(S) and isprime(W) then print(n);
end if:
   end if:
   end do:

Mathematica

pipQ[n_]:=Module[{c=Prime[n]-n-1}, AllTrue[{PrimePi[n], c, PrimePi[ c]}, PrimeQ]]; Select[Prime[Range[30000]], pipQ] (* Requires Mathematica version 10 or later *) (* Harvey P. Dale, Jun 30 2020 *)

Prog

(PARI) isok(p) = isprime(p) && isprime(primepi(p)) && isprime(q=prime(p)-p-1) && isprime(primepi(q)); \\ Michel Marcus, Sep 03 2018

Crossrefs

Cf. A000040, A006450, A318292, A318752.

Sequence in context: A286678 A081479 A335313 * A096996 A256236 A070294

Adjacent sequences: A318748 A318749 A318750 * A318752 A318753 A318754

Keyword

nonn

Author

David James Sycamore, Sep 02 2018

Extensions

Corrected and extended by Harvey P. Dale, Jun 30 2020

Status

approved