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

1,1

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).

Links

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

Formula

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

Example

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

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

Crossrefs

Cf. A018800, A062584.

Sequence in context: A244387 A044334 A044715 * A078787 A160850 A202052

Adjacent sequences: A197813 A197814 A197815 * A197817 A197818 A197819

Keyword

nonn,base,look

Author

Michel Lagneau, Oct 18 2011

Status

approved