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A064901 Semiprimes p1*p2 such that p2 > p1 and p2 mod p1 = 3. 1
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 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,1

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

MATHEMATICA

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

PROG

(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

(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

CROSSREFS

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

Sequence in context: A300094 A342259 A075893 * A039482 A247676 A118159

Adjacent sequences:  A064898 A064899 A064900 * A064902 A064903 A064904

KEYWORD

nonn

AUTHOR

Patrick De Geest, Oct 13 2001

EXTENSIONS

Name clarified by John Cerkan, Apr 13 2018

STATUS

approved

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Last modified June 23 05:11 EDT 2021. Contains 345395 sequences. (Running on oeis4.)