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A178899
Numbers which are both primes and problimes (third definition).
1
2, 7, 11, 19, 23, 43, 53, 73, 79, 97, 103, 109, 127, 139, 151, 157, 163, 181, 193, 199, 211, 1873, 1999, 2017, 2053, 2089, 2143, 2161, 2179, 2251, 2269, 2287, 2341, 2377, 2467, 2503, 2521, 2539, 2557, 2593, 2647, 2683, 2719, 2791, 2917, 2953, 2971, 3061, 3079
OFFSET
1,1
LINKS
M. D. Hirschhorn, How unexpected is the prime number theorem?, Amer. Math. Monthly, 80 (1973), 675-677.
M. D. Hirschhorn, How unexpected is the prime number theorem?, Amer. Math. Monthly, 80 (1973), 675-677. [Annotated scanned copy]
R. C. Vaughan, The problime number theorem, Bull. London Math. Soc., 6 (1974), 337-340.
FORMULA
A000040 INTERSECTION A003068.
MAPLE
b:= proc(n) option remember; local k;
if n=1 then c(2):= 1; 2
else k:= ceil(b(n-1) +1/mul((1-1/b(j)), j=1..n-1));
c(k):= n; k
fi
end:
a:= proc(n) option remember; local k;
if n=1 then b(1)
else for k from c(a(n-1))+1 while not isprime(b(k))
do od; b(k)
fi
end:
seq(a(n), n=1..50); # Alois P. Heinz, Dec 29 2010
MATHEMATICA
nmax = 400;
b[n_] := b[n] = If[n==1, 2, Ceiling[b[n-1]+1/Product[1-1/b[j], {j, 1, n-1}]]];
Intersection[Array[b, nmax], Prime[Range[PrimePi[b[nmax]]]]] (* Jean-François Alcover, Nov 20 2020 *)
CROSSREFS
KEYWORD
nonn
AUTHOR
Jonathan Vos Post, Dec 29 2010
EXTENSIONS
More terms from Alois P. Heinz, Dec 29 2010
STATUS
approved