This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.
%I A380092 #10 Jan 23 2025 12:37:21
%S A380092 1,0,0,0,0,0,0,0,0,0,2,0,0,0,0,0,0,0,0,0,0,0,1,0,0,0,0,0,0,0,0,0,0,0,
%T A380092 0,1,1,0,1,0,0,0,0,0,0,1,0,0,0,0,1,0,0,1,1,2,0,1,0,0,0,0,0,0,0,0,1,0,
%U A380092 0,0,2,0,0,1,0,0,0,0,0,0,0,0,0,1,0,0,0,0,0,0,1,0,0,0,0,0,1,0,1,1,0,0,0,0,0
%N A380092 Number of consecutive primes after prime(n) before their concatenation fails to produce a prime.
%F A380092 a(n) = 0 iff (p_(n+1) - p_n)/2 == 1 (mod 2).
%F A380092 a(n) > 0 iff n is in A030459.
%e A380092 a(1) = 1 since prime(1) = 2 can be concatenated with the next prime 3 to 23 which is prime, but the next concatenation with 5 is 235 which is not prime.
%e A380092 a(2) = 0 since prime(2) = 3 but concatenating the next prime 5 is 35 which is not prime.
%e A380092 a(11) = 2 since prime(11) = 31 concatenates: 3137 is prime, 313741 is prime, but 31374143 is not prime.
%t A380092 a[n_] := Block[{k = 0, p = Prime@ n}, While[ PrimeQ[ FromDigits[ Flatten[ IntegerDigits[ NextPrime[p, Range[0, k]]]]]], k++]; --k]; Array[a, 105]
%Y A380092 Cf. A000040, A030459, A219271, A309191.
%K A380092 easy,nonn,base
%O A380092 1,11
%A A380092 _Robert G. Wilson v_, Jan 12 2025