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A347754 revision #16

A347754
a(n) = sqrt(A347594(n-1)^2 + n^2 + A347594(n)).
5
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
1,1
LINKS
FORMULA
a(n) = floor(sqrt(A347594(n-1)^2 + n^2)) + 1.
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 *)
PROG
(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)
(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
(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
CROSSREFS
Cf. A347594.
Sequence in context: A100993 A117395 A006755 * A005853 A161460 A097029
KEYWORD
nonn
AUTHOR
Seiichi Manyama, Sep 12 2021
STATUS
proposed