A280379 a(n) = A056171(k) - m, where k=prime(n) and m is the Ramanujan prime index to the greatest Ramanujan prime R(m) <= k.

0, 1, 1, 1, 0, 1, 0, 1, 1, 0, 1, 1, 0, 1, 0, 1, 0, 1, 0, 0, 1, 1, 1, 1, 0, 0, 1, 0, 1, 2, 0, 1, 1, 2, 0, 0, 1, 1, 0, 1, 0, 0, 1, 2, 2, 3, 2, 1, 0, 0, 0, 0, 0, 1, 1, 0, 0, 1, 1, 0, 1, 2, 0, 0, 1, 1, 1, 1, 0, 0, 1, 1, 0, 0, 1, 1, 1, 1, 0

Offset: 1

Author

John W. Nicholson, Jan 01 2017

Keywords

• nonn

Comments

a(n)=0 corresponds to the Ramanujan prime R_m = A104272(m) = A056171(k).

Examples

			For prime(30)=113, A056171(113) = 14, 107 is R_12 and 127 is R_13, so 14 -12 = 2 (first occurrence).
		

Crossrefs

Cf. A056171, A104272.

Programs

PARI

\\RR[x] is a list of Ramanujan primes, A104272.
{plimit=1.1*10^4;n=s=0;
forprime(p=2,plimit,
    s++;
    if(p==RR[n+1],n++);
    print1(s-primepi(floor(p/2))-n,", ");
    )
}

Formula

a(n) = A056171(k) - m, where k=prime(n) and m is the Ramanujan prime index to the greatest Ramanujan prime R_m = A104272(m) <= k.