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A240604 Primes p with pi(p), pi(2*p), pi(3*p) and pi(4*p) all prime, where pi(x) denotes the number of primes not exceeding x. 1
10909, 67247, 185869, 408379, 511111, 1297061, 1730461, 1732333, 2135347, 2266079, 2316203, 2978917, 3477737, 4337257, 4495739, 4691849, 6108461, 6407971, 6591163, 7462589, 7909507, 8165039, 8298337, 8948509, 11144083, 11961373, 15019049, 16074059, 16732561, 19316263 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,1

COMMENTS

Conjecture: For any positive integer n, there are infinitely many primes p with pi(k*p) (k = 1,...,n) all prime.

LINKS

Zhi-Wei Sun, Table of n, a(n) for n = 1..2280

Zhi-Wei Sun, Problems on combinatorial properties of primes, preprint, arXiv:1402.6641, 2014.

EXAMPLE

a(1) = 10909 with 10909, pi(10909) = 1327, pi(2*10909) = 2447, pi(3*10909) = 3511 and pi(4*10909) = 4547 all prime.

MATHEMATICA

p[j_, k_]:=p[j, k]=PrimeQ[PrimePi[j*Prime[Prime[k]]]]

p[k_]:=p[k]=p[2, k]&&p[3, k]&&p[4, k]

m=0; Do[If[p[k], m=m+1; Print[m, " ", Prime[Prime[k]]]], {k, 1, 95041}]

CROSSREFS

Cf. A000040, A000720, A006450, A237578, A239428, A239430, A239617.

Sequence in context: A307873 A259138 A082710 * A065322 A166261 A089381

Adjacent sequences:  A240601 A240602 A240603 * A240605 A240606 A240607

KEYWORD

nonn

AUTHOR

Zhi-Wei Sun, Apr 09 2014

STATUS

approved

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Last modified March 8 01:41 EST 2021. Contains 341934 sequences. (Running on oeis4.)