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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.
4
-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
0,3
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).
FORMULA
a(p) = p if and only if p is prime.
EXAMPLE
a(4) = 3 since 43 is prime, a(25) = 13 since 25242322212019181716151413 is prime.
PROG
(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
CROSSREFS
KEYWORD
sign,base
AUTHOR
Chai Wah Wu, Feb 23 2021
STATUS
approved