Brilliant numbers: Difference between revisions

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=={{header|Python}}==

Using primesieve and numpy modules

<lang Python>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)]

primes = [primes(10**n, 10**(n + 1)) for n in range(max_order)]

def smallest_brilliant(~~thresh=0~~):

def smallest_brilliant(lb):

pos = 1

~~for~~ ~~blk~~ ~~in blocks:~~

root = isqrt(lb)

⚫

n = len(blk)

⚫

~~best~~ = blk[-1]**2

~~if best < thresh~~:

for blk in primes:

⚫

n = len(blk)

if blk[-1]*blk[-1] < lb:

pos += n*(n + 1)//2

continue

hi = n - 1

i = np.searchsorted(blk, root, 'left')

~~for~~ i, p ~~in enumerate(~~blk):

i += blk[i]*blk[i] < lb

if (prod := p*p) >= thresh:

~~best = min(prod, best)~~

if not i:

~~break~~

return blk[0]*blk[0], pos

⚫

p = blk[:i + 1]

⚫

q = (lb - 1)//p

idx = np.searchsorted(blk, q, 'right')

~~lo = i~~

sel = idx < n

~~while hi > lo:~~

p, idx = p[sel], idx[sel]

if p*blk[~~(j := (lo + hi)//2)~~] ~~>= thresh:~~

q = blk[idx]

⚫

hi = j

⚫

~~else:~~

⚫

lo = j + 1

~~pos +~~= ~~hi - i~~

sel = q >= p

~~if (prod :~~= p*blk[hi]) >= ~~thresh:~~

p, q, idx = p[sel], q[sel], idx[sel]

best = min(best, prod)

pos += np.sum(idx - np.arange(len(idx)))

return ~~best~~, pos

return np.min(p*q), pos

~~p, first100~~ = 0, []

res = []

p = 0

for i in range(100):

p, ~~pos~~ = smallest_brilliant(p + 1)

p, _ = smallest_brilliant(p + 1)

~~first100~~.append(p)

res.append(p)

print(f'~~First~~ 100: {~~first100~~}')

print(f'first 100 are {res}')

for n in range(2*max_order):

for i in range(max_order*2):

~~p, pos~~ = ~~smallest_brilliant(~~10**n)

thresh = 10**i

p, pos = smallest_brilliant(thresh)

print(f'~~first above~~ 10**{n:2d}: {p:~~18d~~} at ~~position~~ {pos~~:14d~~}')</lang>

print(f'Above 10^{i:2d}: {p:20d} at #{pos}')</lang>

<pre>~~First~~ 100: [4, 6, 9, 10, 14, 15, 21, 25, 35, 49, 121, 143, 169, 187, 209, 221, 247, 253, 289, 299, 319, 323, 341, 361, 377, 391, 403, 407, 437, 451, 473, 481, 493, 517, 527, 529, 533, 551, 559, 583, 589,

<pre>first 100 are [4, 6, 9, 10, 14, 15, 21, 25, 35, 49, 121, 143, 169, 187, 209, 221, 247, 253, 289, 299, 319, 323, 341, 361, 377, 391, 403, 407, 437, 451, 473, 481, 493, 517, 527, 529, 533, 551, 559, 583, 589, 611, 629, 649, 667, 671, 689, 697, 703, 713, 731, 737, 767, 779, 781, 793, 799, 803, 817, 841, 851, 869, 871, 893, 899, 901, 913, 923, 943, 949, 961, 979, 989, 1003, 1007, 1027, 1037, 1067, 1073, 1079, 1081, 1121, 1139, 1147, 1157, 1159, 1189, 1207, 1219, 1241, 1247, 1261, 1271, 1273, 1333, 1343, 1349, 1357, 1363, 1369]

⚫

Above 10^ 0: 4 at #1

611, 629, 649, 667, 671, 689, 697, 703, 713, 731, 737, 767, 779, 781, 793, 799, 803, 817, 841, 851, 869, 871, 893, 899, 901, 913, 923, 943, 949, 961, 979, 989, 1003, 1007, 1027, 1037, 1067, 1073, 1079, 10

Above 10^ 1: 10 at #4

81, 1121, 1139, 1147, 1157, 1159, 1189, 1207, 1219, 1241, 1247, 1261, 1271, 1273, 1333, 1343, 1349, 1357, 1363, 1369]

⚫

Above 10^ 2: 121 at #11

first above 10** 0: 4 at position 1

Above 10^ 3: 1003 at #74

first above 10** 1: 10 at position 4

Above 10^ 4: 10201 at #242

first above 10** 2: 121 at position 11

Above 10^ 5: 100013 at #2505

first above 10** 3: 1003 at position 74

Above 10^ 6: 1018081 at #10538

first above 10** 4: 10201 at position 242

Above 10^ 7: 10000043 at #124364

first above 10** 5: 100013 at position 2505

Above 10^ 8: 100140049 at #573929

first above 10** 6: 1018081 at position 10538

Above 10^ 9: 1000000081 at #7407841

first above 10** 7: 10000043 at position 124364

Above 10^10: 10000600009 at #35547995

first above 10** 8: 100140049 at position 573929

Above 10^11: 100000000147 at #491316167

first above 10** 9: 1000000081 at position 7407841

Above 10^12: 1000006000009 at #2409600866

first above 10**10: 10000600009 at position 35547995

Above 10^13: 10000000000073 at #34896253010

first above 10**11: 100000000147 at position 491316167

Above 10^14: 100000380000361 at #174155363187

first above 10**12: 1000006000009 at position 2409600866

Above 10^15: 1000000000000003 at #2601913448897

first above 10**13: 10000000000073 at position 34896253010

Above 10^16: 10000001400000049 at #13163230391313

first above 10**14: 100000380000361 at position 174155363187

Above 10^17: 100000000000000831 at #201431415980419</pre>

first above 10**15: 1000000000000003 at position 2601913448897

first above 10**16: 10000001400000049 at position 13163230391313

first above 10**17: 100000000000000831 at position 201431415980419 </pre>

=={{header|Raku}}==