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

2, 3, 4, 8, 14, 28, 21, 33, 65, 50, 97, 73, 14, 30, 32, 22, 18, 32, 31, 32, 53, 68, 50, 43, 55, 100, 112, 154, 135, 226, 449, 832, 640, 194, 382, 302, 509, 665, 1213, 905, 213, 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

Offset: 1

Author

Seiichi Manyama, Sep 12 2021

Keywords

• nonn

Links

• Seiichi Manyama, Table of n, a(n) for n = 1..10000

Crossrefs

Cf. A347594.

Programs

Mathematica

b[0]=1;b[m_]:=b[m]=(k=1;While[!IntegerQ@Sqrt[b[m-1]^2+m^2+k],k++];k);
a[n_]:=a[n]=Sqrt[b[n-1]^2+n^2+b[n]];Array[a,100] (* Giorgos Kalogeropoulos, Sep 12 2021 *)

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

Python

from math import isqrt
A347754_list, a = [], 1
for n in range(1,10**3):
    m = a**2+n**2
    k = isqrt(m)+1
    a = k**2-m
    A347754_list.append(k) # Chai Wah Wu, Sep 13 2021

Ruby

def A347754(n)
  s = 1
  ary = []
  (1..n).each{|i|
    j = i * i + s * s
    k = Math.sqrt(j).floor + 1
    ary << k
    s = k * k - j
  }
  ary
end
p A347754(100)

Formula

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