A111183 a(n) = prime(x) - pi(x) where x is the least x such that (prime(x+1) - pi(x+1)) - (prime(x) - pi(x)) = n.

2, 3, 5, 15, 47, 19, 339, 80, 168, 128, 185, 196, 103, 275, 1771, 1871, 1028, 498, 3004, 851, 3641, 1087, 11845, 1613, 5402, 2404, 3182, 2889, 5225, 4190, 5461, 10585, 16958, 1280, 22444, 9357, 56241, 30129, 24857, 19006, 34461, 15852, 224417, 15401

Offset: 1

Author

Cino Hilliard, Oct 22 2005

Keywords

• nonn

Comments

Conjecture: a(n) exists for every n.

Links

• Robert Israel, Table of n, a(n) for n = 1..262

Crossrefs

Cf. A000040, A000720, A111181.

Programs

Maple

N:= 100: # for a(1) .. a(N)
p:= 2: m:= 0: b:= 2:V:= Vector(N): count:= 0:
for x from 2 while count < N do
  p:= nextprime(p);
  if isprime(x) then m:= m+1 fi;
  bp:= b; b:= p-m;
  v:= b-bp;
  if v >= 1 and v <= N and V[v] = 0 then V[v]:= bp; count:= count+1 fi
od:
convert(V,list); # Robert Israel, Mar 16 2025

PARI

a(n) = { for(x=1, oo, my(y=prime(x)-primepi(x), z=prime(x+1)-primepi(x+1)); if(z-y == n,return(y)) ); }