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
Keywords
Examples
There are two composite numbers less than 7, namely, 4 and 6, and 2 is prime. Therefore 7 is a member of the sequence.
Links
- Alois P. Heinz, Table of n, a(n) for n = 1..10000
Crossrefs
Cf. A072677.
Programs
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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 *)
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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
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PARI
listp(nn)=forprime(p=2, nn, if (isprime(p - primepi(p) - 1), print1(p, ", "));); \\ Michel Marcus, Aug 27 2016
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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
Extensions
a(16)-a(61) from Ivan N. Ianakiev, Jul 12 2015