A341701 a(n) = largest m > 0 such that the decimal concatenation n||n-1||n-2||...||m is prime, or -1 if no such prime exists.

-1, -1, 2, 3, 3, 5, -1, 7, -1, -1, 9, 11, -1, 13, -1, -1, -1, 17, -1, 19, -1, -1, 21, 23, 23, 13, -1, 23, -1, 29, -1, 31, -1, -1, 33, -1, -1, 37, -1, -1, -1, 41, 41, 43, -1, -1, 39, 47, 41, -1, -1, 47, 37, 53, -1, 43, 47, -1, 57, 59, 47, 61, -1, -1, -1, -1, -1

Offset: 0

Author

Chai Wah Wu, Feb 23 2021

Keywords

• sign
• base

Comments

A variant of A341717. a(82) = 1. Are there other n such that a(n) = 1?

Similar argument as in A341716 shows that if n > 3 and a(n) >= 0, then a(n) is odd, n-a(n) !== 2 (mod 3) and n+a(n) !== 0 (mod 3).

Examples

			a(4) = 3 since 43 is prime, a(25) = 13 since 25242322212019181716151413 is prime.
		

Crossrefs

Cf. A052088, A052089, A341702, A341715, A341716, A341717.

Programs

Python

from sympy import isprime
def A341701(n):
    k, m = n, n-1
    while not isprime(k) and m > 0:
        k = int(str(k)+str(m))
        m -= 1
    return m+1 if isprime(k) else -1

Formula

a(p) = p if and only if p is prime.