A197816 Smallest composite number m such that m and the greatest prime divisor of m begin with n.

102, 203, 36, 410, 50, 603, 70, 801, 970, 1010, 110, 1270, 130, 1490, 1510, 1630, 170, 1810, 190, 20030, 2110, 2230, 230, 2410, 2510, 2630, 2710, 2810, 290, 3070, 310, 32030, 3310, 3470, 3530, 3670, 370, 3830, 3970, 4010, 410, 4210, 430, 4430, 4570, 4610, 470

Offset: 1

Author

Michel Lagneau, Oct 18 2011

Keywords

• nonn
• base
• look

Comments

A majority of numbers are divisible by 10.

The case m prime gives A062584 (First occurrence of n in the decimal representation of primes).

Examples

			a(6) = 603 = 3^2*67 => 603 and 67 start with 6.
		

Links

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

Crossrefs

Cf. A018800, A062584.

Programs

Maple

with(numtheory): for n from 1 to 47 do: l1:=length(n):i:=0:for m from 2 to 100000 while(i=0) do: x:=factorset(m):k:=nops(x):y:=x[k]: l2:=length(m):x1:=floor(m/(10^(l2-l1))): l3:=length(y):x2:=floor(y/(10^(l3-l1))):if x1=n and x2=n and l2>=l1 and l3 >=l1 and type(m,prime)=false then i:=1: printf(`%d, `,m):else fi :od:od:
# Alternative:
f:= proc(n) local d,k,p;
  for d from 1 do
    for k from 10^d*n to 10^d*(n+1)-1 do
       if not isprime(k) then
         p:= max(numtheory:-factorset(k));
         if p >= n and floor(p/10^(length(p)-length(n))) = n then return k fi
       fi od od
end proc:
map(f, [$1..100]); # Robert Israel, Jun 04 2018

Formula

a(n) = 10*A018800(n) for n >= 9. - Robert Israel, Jun 04 2018