A064907 Semiprimes p1*p2 such that p2 mod p1 = 9, with p2 > p1.

341, 583, 731, 793, 893, 1067, 1469, 1793, 1807, 1943, 2201, 2323, 2483, 2519, 2761, 3043, 3071, 3487, 3497, 3781, 4213, 4439, 4511, 4777, 4841, 4849, 4939, 5497, 5809, 5933, 5947, 6511, 6539, 6989, 7093, 7117, 7391, 7493, 7601, 7613, 7783, 7891, 7967

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

spQ[n_]:=Module[{fi=FactorInteger[n][[All,1]]},PrimeOmega[n]==2&&Mod[ fi[[2]],fi[[1]]]==9]; Select[Range[8000],spQ]//Quiet (* Harvey P. Dale, Aug 02 2019 *)

PARI

isok(n) = my(f = factor(n)); (#f~ == 2) && (vecmax(f[,2]) < 2) && ((f[2,1] % f[1,1]) == 9); \\ Michel Marcus, Apr 16 2018

Python

from sympy import factorint
def is_A064907(n):
    f = factorint(n)
    return (sum([f[i] for i in f]) == 2) and (max(f) % min(f) == 9)
def list_A064907(cnt):
    inx = 0
    n = 1
    an = []
    while inx < cnt:
        if is_A064907(n):
            an.append(n)
            inx += 1
        n += 2
    return an #John Cerkan, Apr 14 2018

Extensions

Offset changed by John Cerkan, Apr 12 2018