A064909 Semiprimes p1*p2 such that p2 > p1 and p2 mod p1 = 11.

481, 1157, 1343, 1921, 2171, 2263, 2369, 2509, 3077, 3097, 3427, 3523, 3683, 4171, 4537, 4541, 4811, 5213, 5263, 5389, 5543, 6107, 6227, 6707, 7123, 7241, 8279, 8593, 8621, 8717, 8857, 8873, 9353, 9607, 10411, 10537, 11359, 11461, 11567, 11747, 11761, 11819

Offset: 1

Author

Patrick De Geest, Oct 13 2001

Keywords

• nonn

Links

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

Crossrefs

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

Programs

Mathematica

pmp11Q[n_]:=Module[{fi=FactorInteger[n][[All,1]]},Mod[fi[[2]],fi[[1]]] == 11]; Select[ Range[12000],PrimeNu[#]==PrimeOmega[#]==2&&pmp11Q[#]&] (* Harvey P. Dale, Jun 25 2018 *)

PARI

isok(n) = my(f = factor(n)); (#f~ == 2) && (vecmax(f[,2]) < 2) && ((f[2,1] % f[1,1]) == 11);

Python

from sympy import factorint
def is_A064909(n):
    f = factorint(n)
    return (sum([f[i] for i in f]) == 2) and (max(f) % min(f) == 11)
def first_A064909(n):
    x = 1
    an = []
    while len(an) < n:
        if is_A064909(x): an.append(x)
        x += 2
    return an # John Cerkan, Apr 14 2018

Extensions

Offset and name fixed by John Cerkan, Apr 12 2018