Data commit

Task/Brilliant-numbers/Python/brilliant-numbers.py

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+from primesieve.numpy import primes
+from math import isqrt
+import numpy as np
+
+max_order = 9
+blocks = [primes(10**n, 10**(n + 1)) for n in range(max_order)]
+
+def smallest_brilliant(lb):
+    pos = 1
+    root = isqrt(lb)
+
+    for blk in blocks:
+        n = len(blk)
+        if blk[-1]*blk[-1] < lb:
+            pos += n*(n + 1)//2
+            continue
+
+        i = np.searchsorted(blk, root, 'left')
+        i += blk[i]*blk[i] < lb
+
+        if not i:
+            return blk[0]*blk[0], pos
+
+        p = blk[:i + 1]
+        q = (lb - 1)//p
+        idx = np.searchsorted(blk, q, 'right')
+
+        sel = idx < n
+        p, idx = p[sel], idx[sel]
+        q = blk[idx]
+
+        sel = q >= p
+        p, q, idx = p[sel], q[sel], idx[sel]
+
+        pos += np.sum(idx - np.arange(len(idx)))
+        return np.min(p*q), pos
+
+res = []
+p = 0
+for i in range(100):
+    p, _ = smallest_brilliant(p + 1)
+    res.append(p)
+
+print(f'first 100 are {res}')
+
+for i in range(max_order*2):
+    thresh = 10**i
+    p, pos = smallest_brilliant(thresh)
+    print(f'Above 10^{i:2d}: {p:20d} at #{pos}')