A243294 Least number k > 1 such that a number composed of k consecutive ascending digits starting with n is prime.

171, 2, 179, 4, 29, 2, 5, 2, 13

Offset: 1

Author

Derek Orr, Jun 02 2014

Keywords

• nonn
• base
• full
• fini

Comments

After the digit 9 comes 0 and it repeats.

If k could equal 1, the sequence becomes {171, 1, 1, 4, 1, 2, 1, 2, 13}.

It is interesting that when n is prime, a(n) is prime.

Examples

			78 is not prime. 789 is not prime. 7890 is not prime. 78901 is prime. Thus a(7) = 5 since 78901 is a 5-digit number.
		

Crossrefs

Cf. A120821.

Programs

PARI

a(n) = {s = Str(n); i = n+1; while (1, if (i==10, i = 0); s = concat(s, i); i++; if (isprime(eval(s)), return (length(s))););} \\ Michel Marcus, Jun 04 2014

Python

import sympy
from sympy import isprime
def a(n):
    num = str(n)
    for i in range(n+1, 10**3):
        num += str(i%10)
        if isprime(int(num)):
            return len(num)
n=1
while n < 10:
    print(a(n), end=', ')
    n+=1