A382277 a(n) is the least composite number obtained by inserting a nonempty string of 0's inside n.

100, 1001, 102, 1003, 104, 105, 106, 1007, 108, 100009, 200, 201, 202, 203, 204, 205, 206, 207, 208, 209, 300, 301, 302, 303, 304, 305, 306, 3007, 308, 309, 400, 40001, 402, 403, 404, 405, 406, 407, 408, 4009, 500, 501, 502, 50003, 504, 505, 506, 507, 508, 50009, 600, 6001, 602, 603, 604, 605

Offset

10,1

Comments

If n is divisible by 3 then one 0 is inserted.

Links

Robert Israel, Table of n, a(n) for n = 10..10000

Example

a(19) = 100009 because 100009 = 7^2 * 13 * 157 is composite while 109, 1009 and 10009 are all prime.

Maple

f:= proc(n) local k, t, i, a, b;
    for k from 1 do
      for i from ilog10(n) to 1 by -1 do
        b:= n mod 10^i;
        a:= (n-b)/10^i;
        t:= a*10^(k+i)+b;
        if not isprime(t) then return t fi;
    od od;
end proc:
map(f, [$10 .. 200]);

Crossrefs

Sequence in context: A173485 A173484 A136387 * A379268 A001737 A266838

Adjacent sequences: A382274 A382275 A382276 * A382278 A382279 A382280

Keyword

nonn,base,look

Author

Robert Israel, Mar 20 2025

Status

approved