A382981 - OEIS

A382981

The smallest n-digit prime that turns composite at each step as its digits are successively appended, starting from the last.

2, 11, 101, 1019, 10007, 100043, 1000003, 10000019, 100000007, 1000000007, 10000000019, 100000000003, 1000000000039, 10000000000037, 100000000000031, 1000000000000037, 10000000000000061, 100000000000000003, 1000000000000000003, 10000000000000000051

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OFFSET

1,1

LINKS

Michael S. Branicky, Table of n, a(n) for n = 1..1000

EXAMPLE

a(4) = 1019, because 1019 is prime and 10199 = 7 * 31 * 47, 101991 = 3 * 33997, 1019910 = 2 * 3 * 5 * 33997 and 10199101 = 11 * 927191 are composite, while no smaller 4-digit prime exhibits this property.

MATHEMATICA

ok[p_] := Block[{d = IntegerDigits@p}, d = Join[d, Reverse@ d]; And @@ CompositeQ /@ (FromDigits[d[[;; #]]] & /@ Range[Length[d]/2 + 1, Length@d])]; a[n_] := Block[{p = NextPrime[10^(n-1)]}, While[! ok[p], p = NextPrime@p]; p]; Array[a, 20] (* Giovanni Resta, Apr 11 2025 *)

PROG

(Python)

from sympy import isprime, nextprime

def c(s): # check if prime p's string of digits meets the concatenation condition

return not any(isprime(int(s:=s+c)) for c in s[::-1])

def a(n):

p = nextprime(10**(n-1))

while not c(str(p)): p = nextprime(p)

return p

print([a(n) for n in range(1, 21)]) # Michael S. Branicky, Apr 16 2025

CROSSREFS

Cf. A003617, A382899.