cp's OEIS Frontend

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

%I A064901 #30 Apr 16 2018 19:10:17
%S A064901 65,115,119,215,217,265,365,377,413,415,511,515,517,565,629,707,779,
%T A064901 815,865,965,1099,1115,1165,1207,1243,1315,1391,1393,1415,1465,1501,
%U A064901 1565,1589,1687,1727,1765,1769,1865,1883,1915,1969,1981,2165,2177,2215
%N A064901 Semiprimes p1*p2 such that p2 > p1 and p2 mod p1 = 3.
%C A064901 The semiprimes must be squarefree, since p1 does not divide p2. - _Michael De Vlieger_, Apr 12 2018
%H A064901 John Cerkan, <a href="/A064901/b064901.txt">Table of n, a(n) for n = 1..10000</a>
%t A064901 Select[Range@ 2215, And[#[[All, -1]] == {1, 1}, Mod[#2, #1] == 3 & @@ #[[All, 1]]] &@ FactorInteger[#] &] (* _Michael De Vlieger_, Apr 12 2018 *)
%o A064901 (Python)
%o A064901 from sympy import factorint
%o A064901 def is_A064901(n):
%o A064901     f = factorint(n)
%o A064901     return (sum([f[i] for i in f]) == 2) and (max(f) % min(f) == 3)
%o A064901 def first_A064901(n):
%o A064901     x = 1
%o A064901     an = []
%o A064901     while len(an) < n:
%o A064901         if is_A064901(x): an.append(x)
%o A064901         x += 2
%o A064901     return an # _John Cerkan_, Apr 14 2018
%o A064901 (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 A064901 Cf. A001358 (p2 mod p1 = 0), A006881, A064899-A064911.
%K A064901 nonn
%O A064901 1,1
%A A064901 _Patrick De Geest_, Oct 13 2001
%E A064901 Name clarified by _John Cerkan_, Apr 13 2018