

A276511


Primes that are equal to the sum of the prime factors of some perfect number.


3




OFFSET

1,1


COMMENTS

Primes of the form 2^n + 2*n  3 such that 2^n  1 is also prime.
Conjectures (defining x = 170141183460469231731687303715884105727 = A007013(4)):
(1) 2^x + 2*x  3 is in this sequence;
(2) a(5) = 2^x + 2*x  3 (see comments of A276493);
(3) primes of A007013 are Mersenne prime exponents A000043, i.e., x is new exponent in A000043.


LINKS

Table of n, a(n) for n=1..4.


EXAMPLE

a(1) = 5 because 2^21 = 3 and 2^2+2*23 = 5 are primes,
a(2) = 11 because 2^31 = 7 and 2^3+2*33 = 11 are primes,
a(3) = 139 because 2^71 = 127 and 2^7+2*73 = 139 are primes.


MAPLE

A276511:=n>`if`(isprime(2^n1) and isprime(2^n+2*n3), 2^n+2*n3, NULL): seq(A276511(n), n=1..10^3); # Wesley Ivan Hurt, Sep 07 2016


PROG

(MAGMA) [2^n+2*n3: n in [1..200]  IsPrime(2^n1) and IsPrime(2^n+2*n3)];


CROSSREFS

Subsequence of A192436.
Cf. A000043, A000396, A000668, A007013, A100118, A276493.
Sequence in context: A083418 A266527 A267078 * A020453 A036932 A162252
Adjacent sequences: A276508 A276509 A276510 * A276512 A276513 A276514


KEYWORD

nonn,more


AUTHOR

JuriStepan Gerasimov, Sep 06 2016


EXTENSIONS

Name suggested by Michel Marcus, Sep 07 2016


STATUS

approved



