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A243894 a(n) = prime(k+1) with k = n^2 + prime(n)^2.

%I A243894 #14 Nov 09 2024 18:09:31
%S A243894 13,43,149,317,853,1277,2281,2957,4507,7433,8693,12671,15887,17839,
%T A243894 21701,28099,35407,38327,46997,53359,56911,67511,75289,87541,105173,
%U A243894 115067,120473,130829,136573,147919,189139,202519,223009,230449,267413,275711
%N A243894 a(n) = prime(k+1) with k = n^2 + prime(n)^2.
%C A243894 The prime numbers prime(k-1) = A243893, prime(k) = A243892 and a(n) = prime(k+1) with k = n^2 + prime(n)^2 are forming a triple of successive prime numbers.
%H A243894 Freimut Marschner, <a href="/A243894/b243894.txt">Table of n, a(n) for n = 1..63</a>
%F A243894 a(n) = prime((n^2 + prime(n)^2) + 1) = prime(A106587(n) + 1).
%e A243894 n=1, n^2 = 1, prime(1) = 2, 2^2 = 4, 1 + 4 = 5, 5 + 1 = 6, prime(6) = 13 ;
%e A243894 n=2, n^2 = 4, prime(2) = 3, 3^2 = 9, 4 + 9 = 13, 13 + 1 = 14, prime(14) = 43.
%t A243894 Table[Prime[n^2+Prime[n]^2+1],{n,40}] (* _Harvey P. Dale_, Dec 31 2015 *)
%o A243894 (PARI) vector(40, n, prime(n^2 + prime(n)^2 + 1)) \\ _Colin Barker_, Jun 14 2014
%Y A243894 Cf. A000290 (squares n^2), A000040 (prime(n)), A001248 (prime(n)^2), A106587 (n^2 + prime(n)^2).
%K A243894 nonn
%O A243894 1,1
%A A243894 _Freimut Marschner_, Jun 14 2014