A073435 Smallest x such that remainder if x-th composite is divided by pi(x) equals n.

4, 7, 8, 13, 30, 17, 35, 23, 40, 50, 53, 51, 55, 52, 63, 60, 68, 69, 146, 76, 154, 83, 156, 162, 172, 177, 185, 109, 195, 187, 192, 188, 189, 190, 208, 209, 210, 214, 215, 216, 217, 230, 218, 219, 220, 224, 225, 251, 248, 249, 250, 255, 256, 262, 267, 280, 289

Offset: 1

Author

Labos Elemer, Jul 31 2002

Keywords

• nonn
• look

Examples

			Remainder=4 appears first as Mod[c[13],Pi[13]]=Mod[22,6]=4, so a(4)=13.
		

Links

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

Crossrefs

Cf. A000720, A002808, A065861.

Programs

Maple

N:= 100: m:= 1: V:= Vector(N): count:= 0:
for n from 6 while count < N do
  if not isprime(n) then
    m:= m+1;
    t:= n mod numtheory:-pi(m);
    if t > 0 and t <= N and V[t] = 0 then
      count:= count+1; V[t]:= m
    fi
  fi
od:
convert(V,list); # Robert Israel, May 21 2020

Formula

a(n) = Min{x; Mod[A002808(x), A000720(x)]=n} = Min{x; A065861(x)=n}.