A197816 - OEIS

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

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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.