A272862 Positive integers j such that prime(i) + prime(j) = i*j for some i <= j.

4, 6, 8, 24, 29, 30, 164, 165, 166, 1051, 2624, 2638, 2650, 2670, 2674, 2676, 40027, 40028, 40112, 251701, 251703, 251706, 251751, 637144, 637202, 637216, 637220, 1617162, 1617165, 4124694, 10553383, 10553408, 10553464, 10553533, 10553535, 10553839, 69709686

Offset: 1

Author

Giuseppe Coppoletta, Jul 25 2016

Keywords

• nonn

Comments

Also pi(q) for primes q verifying p+q = pi(p)*pi(q) for some prime p <= q.

The list of products i*j gives A272860. See also comments there.

Examples

			8 is a term as prime(3) + prime(8) = 3*8.
		

Links

• Giuseppe Coppoletta, Table of n, a(n) for n = 1..43

Crossrefs

Cf. A272860, A272861, A000720, A000040.

Programs

Mathematica

Select[Range[3000], Function[j, Total@ Boole@ Map[Prime@ # + Prime@ j == # j &, Range@ j] > 0]] (* Michael De Vlieger, Jul 28 2016 *)

PARI

is(n) = for(i=1, n, if(prime(i)+prime(n)==i*n, return(1))); return(0) \\ Felix Fröhlich, Jul 27 2016

PARI

is(n,p=prime(n))=my(i); forprime(q=2,p, if(i++*n==p+q, return(1))); 0
v=List(); n=0; forprime(p=2,1e6, if(is(n++,p), listput(v,n))); Vec(v) \\ Charles R Greathouse IV, Jul 28 2016

Sage

def sol(n):
    if n<5: a=n
    else: a=exp(n+1)/(n+1)
    b=(n-1)/n^2*exp(n^2/(n-1.1))
    return [j for j in range(a,b) if is_prime(n*j-nth_prime(n)) and prime_pi(n*j-nth_prime(n))==j]
flatten([sol(i) for i in (1..15) if len(sol(i))>0]) #