A262741 Composite odd numbers m such that q == -1 (mod p) for at least one pair (p, q) < m satisfying the following two conditions: p is a prime divisor of m, and if a prime divides q then it divides m. These are called absent numbers.
15, 33, 45, 51, 63, 65, 69, 75, 87, 91, 95, 99, 105, 123, 135, 141, 145, 147, 153, 159, 165, 175, 177, 189, 195, 207, 213, 221, 225, 231, 245, 249, 255, 261, 267, 273, 285, 287, 295, 297, 303, 315, 321, 325, 339, 345, 357, 363, 369, 375, 385, 393, 395, 399
Offset: 1
Keywords
Links
- Serafín Ruiz-Cabello, On the use of the lowest common multiple to build a prime-generating recurrence, arXiv:1504.05041 [math.CO], 2015.
Programs
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Sage
def triangle(q, m): # This is the first auxiliary program if q >= m: return False Q = factor(q) for par in Q: if m % par[0] != 0: return False return True def pairs(m): # This is the second auxiliary program L = [] M = factor(m) for par in M: p = par[0] for q in range(p-1, m, p): if triangle(q, m): L.append((p, q)) return L def print_absents(n0, n): # This program gives a list with every absent number in the interval [n0,n] L = [] m0 = n0+1-(n0%2) for m in range(m0, n+1, 2): if not is_prime(m): if pairs(m) != []: L.append(m) return L # Serafín Ruiz-Cabello, Sep 30 2015
Comments