cp's OEIS Frontend

A341932 a(n) = largest k < n such that the decimal concatenation n||n-1||n-2||...||n-k is prime, or -1 if no such prime exists.

%I A341932 #12 Jul 29 2023 11:19:36
%S A341932 -1,-1,0,0,1,0,-1,4,-1,-1,3,0,-1,0,-1,-1,-1,0,-1,0,-1,-1,3,0,1,12,-1,
%T A341932 4,-1,0,-1,0,-1,-1,1,-1,-1,0,-1,-1,-1,0,1,0,-1,-1,43,0,31,-1,-1,4,15,
%U A341932 12,-1,28,9,-1,1,0,13,0,-1,-1,-1,-1,-1,0,57,-1,1,0,-1
%N A341932 a(n) = largest k < n such that the decimal concatenation n||n-1||n-2||...||n-k is prime, or -1 if no such prime exists.
%C A341932 a(82) = 81, are there any other n such that a(n) = n-1?
%C A341932 Primes p such that a(p) > 0: 7, 53, 73, 79, 89, 103, ...
%C A341932 n such that a(n) > A341702(n): 7, 10, 22, 46, 48, 53, 55, 73, ...
%C A341932 Similar argument as in A341716 shows that if n > 3 and a(n) >= 0, then n-a(n) is odd, a(n) !== 2 (mod 3) and 2n-a(n) !== 0 (mod 3).
%F A341932 a(n) = n-A341931(n) >= A341702(n).
%e A341932 a(22) = 3 since 22212019 is prime.
%o A341932 (Python)
%o A341932 from sympy import isprime
%o A341932 def A341932(n):
%o A341932     k, m, r = n, n-1, 0 if isprime(n) else -1
%o A341932     while m > 0:
%o A341932         k = int(str(k)+str(m))
%o A341932         if isprime(k):
%o A341932             r = n-m
%o A341932         m -= 1
%o A341932     return r
%Y A341932 Cf. A052088, A052089, A341701, A341702, A341715, A341716, A341717, A341931.
%K A341932 sign,base
%O A341932 0,8
%A A341932 _Chai Wah Wu_, Feb 23 2021