A064901 - OEIS

%I #30 Apr 16 2018 19:10:17

%S 65,115,119,215,217,265,365,377,413,415,511,515,517,565,629,707,779,

%T 815,865,965,1099,1115,1165,1207,1243,1315,1391,1393,1415,1465,1501,

%U 1565,1589,1687,1727,1765,1769,1865,1883,1915,1969,1981,2165,2177,2215

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

%C The semiprimes must be squarefree, since p1 does not divide p2. - _Michael De Vlieger_, Apr 12 2018

%H John Cerkan, <a href="/A064901/b064901.txt">Table of n, a(n) for n = 1..10000</a>

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

%o (Python)

%o from sympy import factorint

%o def is_A064901(n):

%o     f = factorint(n)

%o     return (sum([f[i] for i in f]) == 2) and (max(f) % min(f) == 3)

%o def first_A064901(n):

%o     x = 1

%o     an = []

%o     while len(an) < n:

%o         if is_A064901(x): an.append(x)

%o         x += 2

%o     return an # _John Cerkan_, Apr 14 2018

%o (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

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

%K nonn

%O 1,1

%A _Patrick De Geest_, Oct 13 2001

%E Name clarified by _John Cerkan_, Apr 13 2018