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A065117
Primes such that prime(p) +- pi(p) are simultaneously prime.
1
3, 113, 463, 593, 743, 1109, 2473, 4139, 4657, 4937, 5531, 5879, 6473, 6581, 6659, 6701, 7297, 7529, 8387, 8521, 8929, 9349, 10369, 10499, 12289, 12829, 13411, 13697, 14033, 14323, 15907, 18637, 19391, 19841, 21143, 21647, 23021, 27077
OFFSET
1,1
COMMENTS
Intersection of A065059 and A065060.
LINKS
EXAMPLE
113 is in the sequence because PrimePi(113) is 30, Prime(113) is 617, and both 587 and 647 are primes.
MATHEMATICA
Do[p0 = Prime[ Prime[n]]; p1 = PrimePi[ Prime[n]]; If[ PrimeQ[p0 + p1] && PrimeQ[p0 - p1], Print[ Prime[n]]], {n, 1, 5000} ]
spQ[n_]:=Module[{p=PrimePi[n]}, AllTrue[Prime[n]+{p, -p}, PrimeQ]]; Select[ Prime[ Range[10000]], spQ] (* Requires Mathematica version 10 or later *) (* Harvey P. Dale, Sep 03 2018 *)
PROG
(PARI) { n=0; default(primelimit, 4294965247); for (m=1, 10^9, p=prime(m); p0 = prime(p); p1 = primepi(p); if (isprime(p0 + p1) && isprime(p0 - p1), write("b065117.txt", n++, " ", p); if (n==1000, return)) ) } \\ Harry J. Smith, Oct 10 2009
CROSSREFS
Sequence in context: A249164 A341047 A080174 * A227794 A225334 A240441
KEYWORD
nonn
AUTHOR
Robert G. Wilson v, Nov 12 2001
EXTENSIONS
Example corrected by Harvey P. Dale, Sep 03 2018
STATUS
approved