A358154 a(n) is the smallest composite number obtained by appending one or more 1's to n.

111, 21, 3111, 411, 51, 611, 711, 81, 91, 1011, 111, 121, 1311, 141, 15111, 161, 171, 18111, 1911, 201, 21111, 221, 231, 24111, 2511, 261, 27111, 2811, 291, 301, 3111, 321, 3311, 341, 351, 361, 371, 381, 391, 4011, 411, 42111, 4311, 441, 451, 4611, 471, 481, 4911, 501, 511, 5211, 531, 5411

Offset: 1

Author

Gleb Ivanov, Nov 01 2022

Keywords

• nonn
• base

Comments

a(n) is either 10*n+1, 100*n+11 or 1000*n+111, because at least one of these is divisible by 3. - Robert Israel, Nov 01 2022

Actually: exactly one of these is divisible by 3. Almost all terms are a(n) = 10n + 1: this is the case for about (k-1)/k of the terms up to 10^k (i.e., 69% ~ 2/3 up to 10^3, 76% = 3/4 up to 10^4, 80% = 4/5 up to 10^5, 83% = 5/6 up to 10^6). - M. F. Hasler, Nov 03 2022

Crossrefs

Cf. A069568, A112386, A002808, A153275.

Programs

Maple

f:= proc(n) local x;
   x:= n;
   do
     x:= 10*x+1;
     if not isprime(x) then return x fi;
   od
end proc:
map(f, [$1..100]); # Robert Israel, Nov 01 2022

Mathematica

a[n_] := NestWhile[10*# + 1 &, 10*n + 1, ! CompositeQ[#] &]; Array[a, 54] (* Amiram Eldar, Nov 01 2022 *)

PARI

a(n) = my(d=digits(n), m); if (!isprime(n), d = concat(d, 1)); while(isprime(m=fromdigits(d)), d=concat(d, 1)); m; \\ Michel Marcus, Nov 01 2022

Python

from sympy import isprime
def A358154(n):
    t = str(n)+'1'
    while isprime(int(t)):t=t+'1'
    return int(t)
print([A358154(i) for i in range(1, 100)])