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A378904 2*a(n) are the gaps that correspond to A350100(n).

%I A378904 #17 Jan 04 2025 16:10:49
%S A378904 1,2,3,7,9,10,12,13,15,17,18,20,26,27,29,33,39,41,66,75,84,90,95,100,
%T A378904 113,126,140,144,155,162,177,204,206,210,216,302,303,364,389,391,399,
%U A378904 418,441,469,492,497,504,520,613,723
%N A378904 2*a(n) are the gaps that correspond to A350100(n).
%o A378904 (PARI) a378904(kmax) = my(d=0); for(k=2, kmax, my(k2=k*k, dd=(nextprime(k2)-precprime(k2))/2); if(dd>d, print1(dd,", "); d=dd));
%o A378904 a378904(10^6)
%o A378904 (Python)
%o A378904 from itertools import count, islice
%o A378904 from sympy import prevprime, nextprime
%o A378904 def A378904_gen(): # generator of terms
%o A378904     c = 0
%o A378904     for k in count(2):
%o A378904         a = nextprime(m:=k**2)-prevprime(m)
%o A378904         if a>c:
%o A378904             yield a>>1
%o A378904             c = a
%o A378904 A378904_list = list(islice(A378904_gen(),20)) # _Chai Wah Wu_, Dec 17 2024
%Y A378904 Cf. A058043, A350100.
%K A378904 nonn,more
%O A378904 1,2
%A A378904 _Hugo Pfoertner_, Dec 15 2024
%E A378904 a(50) from _Hugo Pfoertner_, Jan 04 2025