A064901 Semiprimes p1*p2 such that p2 > p1 and p2 mod p1 = 3.

65, 115, 119, 215, 217, 265, 365, 377, 413, 415, 511, 515, 517, 565, 629, 707, 779, 815, 865, 965, 1099, 1115, 1165, 1207, 1243, 1315, 1391, 1393, 1415, 1465, 1501, 1565, 1589, 1687, 1727, 1765, 1769, 1865, 1883, 1915, 1969, 1981, 2165, 2177, 2215

Offset: 1

Author

Patrick De Geest, Oct 13 2001

Keywords

• nonn

Comments

The semiprimes must be squarefree, since p1 does not divide p2. - Michael De Vlieger, Apr 12 2018

Links

• John Cerkan, Table of n, a(n) for n = 1..10000

Crossrefs

Cf. A001358 (p2 mod p1 = 0), A006881, A064899-A064911.

Programs

Mathematica

Select[Range@ 2215, And[#[[All, -1]] == {1, 1}, Mod[#2, #1] == 3 & @@ #[[All, 1]]] &@ FactorInteger[#] &] (* Michael De Vlieger, Apr 12 2018 *)

PARI

isok(n) = my(f = factor(n)); (#f~ == 2) && (vecmax(f[,2]) < 2) && ((f[2,1] % f[1,1]) == 3); \\ Michel Marcus, Apr 16 2018

Python

from sympy import factorint
def is_A064901(n):
    f = factorint(n)
    return (sum([f[i] for i in f]) == 2) and (max(f) % min(f) == 3)
def first_A064901(n):
    x = 1
    an = []
    while len(an) < n:
        if is_A064901(x): an.append(x)
        x += 2
    return an # John Cerkan, Apr 14 2018

Extensions

Name clarified by John Cerkan, Apr 13 2018