A178899 Numbers which are both primes and problimes (third definition).
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
Keywords
Links
- Alois P. Heinz, Table of n, a(n) for n = 1..1000
- 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.
Programs
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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 *)
Extensions
More terms from Alois P. Heinz, Dec 29 2010