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A197816
Smallest composite number m such that m and the greatest prime divisor of m begin with n.
2
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
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
Sequence in context: A244387 A044334 A044715 * A078787 A160850 A202052
KEYWORD
nonn,base,look
AUTHOR
Michel Lagneau, Oct 18 2011
STATUS
approved