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

1,1

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.

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

Cf. A000040, A003068, A178532.

Sequence in context: A166862 A105881 A060191 * A023393 A084619 A236478

Adjacent sequences: A178896 A178897 A178898 * A178900 A178901 A178902

Keyword

nonn

Author

Jonathan Vos Post, Dec 29 2010

Extensions

More terms from Alois P. Heinz, Dec 29 2010

Status

approved