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A347754 a(n) = sqrt(A347594(n-1)^2 + n^2 + A347594(n)).

%I A347754 #18 Sep 14 2021 03:56:04
%S A347754 2,3,4,8,14,28,21,33,65,50,97,73,14,30,32,22,18,32,31,32,53,68,50,43,
%T A347754 55,100,112,154,135,226,449,832,640,194,382,302,509,665,1213,905,213,
%U A347754 43,57,113,49,99,126,217,269,269,173,116,153,161,212,309,540,1057,863,1690,3157,2593,1343,1401,1506,1797,2829,1170,87
%N A347754 a(n) = sqrt(A347594(n-1)^2 + n^2 + A347594(n)).
%H A347754 Seiichi Manyama, <a href="/A347754/b347754.txt">Table of n, a(n) for n = 1..10000</a>
%F A347754 a(n) = floor(sqrt(A347594(n-1)^2 + n^2)) + 1.
%t A347754 b[0]=1;b[m_]:=b[m]=(k=1;While[!IntegerQ@Sqrt[b[m-1]^2+m^2+k],k++];k);
%t A347754 a[n_]:=a[n]=Sqrt[b[n-1]^2+n^2+b[n]];Array[a,100] (* _Giorgos Kalogeropoulos_, Sep 12 2021 *)
%o A347754 (Ruby)
%o A347754 def A347754(n)
%o A347754   s = 1
%o A347754   ary = []
%o A347754   (1..n).each{|i|
%o A347754     j = i * i + s * s
%o A347754     k = Math.sqrt(j).floor + 1
%o A347754     ary << k
%o A347754     s = k * k - j
%o A347754   }
%o A347754   ary
%o A347754 end
%o A347754 p A347754(100)
%o A347754 (Python)
%o A347754 from math import isqrt
%o A347754 A347754_list, a = [], 1
%o A347754 for n in range(1,10**3):
%o A347754     m = a**2+n**2
%o A347754     k = isqrt(m)+1
%o A347754     a = k**2-m
%o A347754     A347754_list.append(k) # _Chai Wah Wu_, Sep 13 2021
%o A347754 (PARI) lista(nn) = {my(prec = 1, list=List(), x); for (n=1, nn, my(k = 1); while (!issquare(x = prec^2+n^2+k), k++); listput(list, sqrtint(x)); prec = k;); Vec(list);} \\ _Michel Marcus_, Sep 13 2021
%Y A347754 Cf. A347594.
%K A347754 nonn
%O A347754 1,1
%A A347754 _Seiichi Manyama_, Sep 12 2021