A175220 The fifth nonprimes after the primes.

10, 10, 12, 14, 18, 20, 24, 25, 28, 35, 36, 44, 48, 49, 52, 58, 65, 66, 74, 77, 78, 85, 88, 94, 104, 108, 110, 114, 115, 118, 133, 136, 143, 144, 155, 156, 162, 169, 172, 178, 185, 186, 198, 200, 203, 204, 216, 230, 234, 235, 238, 245, 246, 256, 262, 268, 275

Offset: 1

Author

Jaroslav Krizek, Mar 06 2010

Keywords

• nonn

Comments

From Robert Israel, Jul 05 2016: (Start)

For n>1, there are the following cases:

If prime(n)+2 and prime(n)+4 are composite, then a(n) = prime(n)+5.

If exactly one of prime(n)+2 and prime(n)+4 is prime, and prime(n)+6 is composite, then a(n) = prime(n) + 6.

Otherwise, a(n) = prime(n) + 7. (End)

Links

• Robert Israel, Table of n, a(n) for n = 1..10000

Programs

Maple

N:= 1000: # to get all entries <= N
Primes:= select(isprime, [2,seq(i,i=3..N+7,2)]):
nprimes:= nops(Primes):
A[1]:= 10:
A[2]:= 10:
for i from 3 to nprimes-1 do
  p:= Primes[i];
  if p + 5 > N then break fi;
  if Primes[i+1] > p + 4 then A[i]:= p + 5
  elif (i = nprimes-1 or Primes[i+2] <> p+6) and p+6 <= N  then A[i]:= p + 6
  elif p+7 <= N then A[i]:= p + 7
  else break
  fi
od:
seq(A[j],j=1..i-1); # Robert Israel, Jul 05 2016