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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.

%I A341701 #9 Feb 24 2021 08:21:52
%S A341701 -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,
%T A341701 13,-1,23,-1,29,-1,31,-1,-1,33,-1,-1,37,-1,-1,-1,41,41,43,-1,-1,39,47,
%U A341701 41,-1,-1,47,37,53,-1,43,47,-1,57,59,47,61,-1,-1,-1,-1,-1
%N 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.
%C A341701 A variant of A341717. a(82) = 1. Are there other n such that a(n) = 1?
%C A341701 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).
%F A341701 a(p) = p if and only if p is prime.
%e A341701 a(4) = 3 since 43 is prime, a(25) = 13 since 25242322212019181716151413 is prime.
%o A341701 (Python)
%o A341701 from sympy import isprime
%o A341701 def A341701(n):
%o A341701     k, m = n, n-1
%o A341701     while not isprime(k) and m > 0:
%o A341701         k = int(str(k)+str(m))
%o A341701         m -= 1
%o A341701     return m+1 if isprime(k) else -1
%Y A341701 Cf. A052088, A052089, A341702, A341715, A341716, A341717.
%K A341701 sign,base
%O A341701 0,3
%A A341701 _Chai Wah Wu_, Feb 23 2021