A229270 -id:A229270 - cp's OEIS frontend

A229269 Numbers k for which k - k' is prime, k' being the arithmetic derivative of k.

3, 9, 10, 14, 15, 21, 26, 33, 35, 38, 39, 50, 51, 62, 65, 66, 69, 70, 77, 78, 86, 91, 93, 95, 102, 110, 111, 114, 122, 123, 129, 130, 133, 138, 146, 154, 159, 161, 170, 174, 190, 201, 203, 206, 209, 213, 215, 217, 218, 221, 222, 230, 238, 249, 258, 278, 282, 287

Offset: 1

Paolo P. Lava, Sep 18 2013

nonn

			15 is in the list because 15’ = 8 and 15 - 8 = 7 that is prime.

Paolo P. Lava, Table of n, a(n) for n = 1..1000

Cf. A003415, A165561, A165562, A229270-A229272.

with(numtheory); P:=proc(q) local a,n,p; for n from 1 to q do
a:=n*add(op(2,p)/op(1,p),p=ifactors(n)[2]); if isprime(n-a) then print(n); fi; od; end: P(10^5);

from sympy import isprime, factorint
A229269 = [n for n in range(1,10**4) if isprime(n-sum([int(n*e/p) for p,e in factorint(n).items()]))] # Chai Wah Wu, Aug 21 2014

A229272 Numbers n for which n' + n and n' - n are both prime, n' being the arithmetic derivative of n.

Original entry on oeis.org

210, 330, 390, 690, 798, 966, 1110, 1230, 2190, 2310, 2730, 3270, 4110, 4530, 4890, 5430, 6090, 6270, 6810, 6990, 7230, 7890, 8310, 8490, 9030, 9210, 9282, 10470, 10590, 10770, 12090, 12210, 12270, 12570, 12810, 12930, 13110, 13830, 14070, 17070, 17094, 17310

Offset: 1

Paolo P. Lava, Sep 18 2013

nonn

Intersection of A165561 and A229270.

Paolo P. Lava, Table of n, a(n) for n = 1..300

Cf. A003415, A165561, A165562, A229269-A229271.

with(numtheory); P:=proc(q) local a,n,p; for n from 1 to q do
a:=n*add(op(2,p)/op(1,p),p=ifactors(n)[2]);
if isprime(a+n) and isprime(a-n) then print(n); fi;
od; end: P(10^5);

from sympy import isprime, factorint
A229272 = []
for n in range(1, 10**5):
    np = sum([int(n*e/p) for p, e in factorint(n).items()]) if n > 1 else 0
    if isprime(np+n) and isprime(np-n):
        A229272.append(n)
# Chai Wah Wu, Aug 21 2014

A229271 Numbers k for which k + k' and k - k' are both prime, k' being the arithmetic derivative of k.

Original entry on oeis.org

10, 14, 15, 21, 26, 33, 35, 38, 51, 65, 66, 78, 86, 93, 102, 110, 111, 123, 161, 201, 203, 206, 209, 215, 221, 230, 258, 278, 282, 321, 371, 374, 395, 398, 402, 413, 438, 470, 471, 485, 530, 533, 543, 545, 551, 590, 626, 671, 678, 698, 723, 755, 779, 803, 815

Offset: 1

Paolo P. Lava, Sep 18 2013

nonn

Intersection of A165561 and A229269.

Paolo P. Lava, Table of n, a(n) for n = 1..1000

Cf. A003415, A165561, A165562, A229269, A229270, A229272.

with(numtheory); P:=proc(q) local a,n,p; for n from 1 to q do
a:=n*add(op(2,p)/op(1,p),p=ifactors(n)[2]);
if isprime(n+a) and isprime(n-a) then print(n); fi;
od; end: P(10^5);

cp's OEIS Frontend

A229269 Numbers k for which k - k' is prime, k' being the arithmetic derivative of k.

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Maple

Python

A229272 Numbers n for which n' + n and n' - n are both prime, n' being the arithmetic derivative of n.

Views

Author

Keywords

Comments

Links

Crossrefs

Programs

Maple

Python

A229271 Numbers k for which k + k' and k - k' are both prime, k' being the arithmetic derivative of k.

Views

Author

Keywords

Comments

Links

Crossrefs

Programs

Maple