A255769 Primes p such that there are a prime number of composite numbers less than p.

7, 11, 23, 31, 47, 59, 67, 83, 97, 109, 137, 149, 167, 179, 197, 211, 233, 269, 331, 347, 353, 367, 389, 419, 431, 439, 587, 617, 739, 751, 829, 859, 907, 919, 977, 991, 1009, 1031, 1039, 1063, 1117, 1171, 1187, 1237, 1319, 1327, 1427, 1447, 1471, 1499, 1553, 1567, 1723, 1901, 1913, 1933, 2207, 2221, 2269, 2293, 2333

Offset

1,1

Links

Alois P. Heinz, Table of n, a(n) for n = 1..10000

Example

There are two composite numbers less than 7, namely, 4 and 6, and 2 is prime. Therefore 7 is a member of the sequence.

Maple

c:= proc(n) option remember; `if`(n<4, 0,
      c(n-1)+`if`(isprime(n-1), 0, 1))
    end:
a:= proc(n) option remember; local p;
      p:= `if`(n=1, 1, a(n-1));
      do p:= nextprime(p);
         if isprime(c(p)) then break fi
      od; p
    end:
seq(a(n), n=1..100);  # Alois P. Heinz, Jul 23 2015

Mathematica

fQ[n_]:=PrimeQ[n-PrimePi[n]-1]; Select[Prime[Range@400], fQ[#]&] (* Ivan N. Ianakiev, Jul 12 2015 *)

Prog

(PARI) is_ok(n)=my(i, k=0); for(i=2, n-1, if(bigomega(i)>1, k++)); isprime(k)&&isprime(n);
first(m)=my(i=1, v=vector(m), k=0); while(i<=m, if(is_ok(k), v[i]=k; i++); k++); v; \\ Anders Hellström, Jul 29 2015
(PARI) listp(nn)=forprime(p=2, nn, if (isprime(p - primepi(p) - 1), print1(p, ", ")); ); \\ Michel Marcus, Aug 27 2016
(PARI) list(lim)=my(v=List(), n=1); forprime(p=2, lim, if(isprime(p - n++), listput(v, p))); Vec(v) \\ Charles R Greathouse IV, Aug 28 2016

Crossrefs

Cf. A072677.

Sequence in context: A271043 A089056 A210981 * A175625 A082496 A239733

Adjacent sequences: A255766 A255767 A255768 * A255770 A255771 A255772

Keyword

nonn

Author

Antonio Gimenez, Jul 11 2015

Extensions

a(16)-a(61) from Ivan N. Ianakiev, Jul 12 2015

Status

approved