A197816 - OEIS

%I #11 Jun 04 2018 17:54:09

%S 102,203,36,410,50,603,70,801,970,1010,110,1270,130,1490,1510,1630,

%T 170,1810,190,20030,2110,2230,230,2410,2510,2630,2710,2810,290,3070,

%U 310,32030,3310,3470,3530,3670,370,3830,3970,4010,410,4210,430,4430,4570,4610,470

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

%C A majority of numbers are divisible by 10.

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

%H Robert Israel, <a href="/A197816/b197816.txt">Table of n, a(n) for n = 1..10000</a>

%F a(n) = 10*A018800(n) for n >= 9. - _Robert Israel_, Jun 04 2018

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

%p 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:

%p # Alternative:

%p f:= proc(n) local d,k,p;

%p   for d from 1 do

%p     for k from 10^d*n to 10^d*(n+1)-1 do

%p        if not isprime(k) then

%p          p:= max(numtheory:-factorset(k));

%p          if p >= n and floor(p/10^(length(p)-length(n))) = n then return k fi

%p        fi od od

%p end proc:

%p map(f, [$1..100]); # _Robert Israel_, Jun 04 2018

%Y Cf. A018800, A062584.

%K nonn,base,look

%O 1,1

%A _Michel Lagneau_, Oct 18 2011