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

1,1

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

Links

Table of n, a(n) for n=1..54.

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 *)

Prog

(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)])
(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

Crossrefs

Cf. A069568, A112386, A002808, A153275.

Sequence in context: A282804 A283376 A290233 * A279799 A279940 A279996

Adjacent sequences: A358151 A358152 A358153 * A358155 A358156 A358157

Keyword

nonn,base

Author

Gleb Ivanov, Nov 01 2022

Status

approved