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A376992 a(n) is the least n-digit prime of the form j^2 + (j+1)^2.

%I A376992 #19 Oct 14 2024 02:55:33
%S A376992 5,13,113,1013,10513,100801,1006781,10030721,100040513,1001057513,
%T A376992 10000515313,100016728501,1000078402181,10000013617661,
%U A376992 100000472012281,1000000064846161,10000005481873013,100000002459693601,1000000116852093013,10000000062611784481,100000001234170737761
%N A376992 a(n) is the least n-digit prime of the form j^2 + (j+1)^2.
%F A376992 Conjecture: a(n+1)/a(n) ~ 10.
%p A376992 f:= proc(n) local j,x;
%p A376992      for j from ceil((sqrt(2*10^(n-1)-1)-1)/2) do
%p A376992        x:= j^2 + (j+1)^2;
%p A376992        if isprime(x) then return x fi
%p A376992      od
%p A376992 end proc:
%p A376992 map(f, [$1..40]); # _Robert Israel_, Oct 13 2024
%t A376992 a[n_]:=Module[{k=1}, While[!PrimeQ[m=2k^2+2k+1]||IntegerLength[m]<n, k++]; m]; Array[a, 15]
%o A376992 (Python)
%o A376992 from math import isqrt
%o A376992 from itertools import count
%o A376992 from sympy import prime
%o A376992 def A376992(n):
%o A376992     for k in count(isqrt(((a:=10**(n-1))<<1)-1>>2)):
%o A376992         m = 2*k*(k+1)+1
%o A376992         if m >= a and isprime(m):
%o A376992             return m # _Chai Wah Wu_, Oct 13 2024
%Y A376992 Cf. A001844, A027861, A027862, A376907, A376993.
%K A376992 nonn,base
%O A376992 1,1
%A A376992 _Stefano Spezia_, Oct 11 2024