A276511 Primes that are equal to the sum of the prime factors of some perfect number.

5, 11, 139, 170141183460469231731687303715884105979

Offset: 1

Author

Juri-Stepan Gerasimov, Sep 06 2016

Keywords

• nonn
• more

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.

Examples

			a(1) = 5 because 2^2-1 = 3 and 2^2+2*2-3 = 5 are primes,
a(2) = 11 because 2^3-1 = 7 and 2^3+2*3-3 = 11 are primes,
a(3) = 139 because 2^7-1 = 127 and 2^7+2*7-3 = 139 are primes.
		

Crossrefs

Subsequence of A192436.

Cf. A000043, A000396, A000668, A007013, A100118, A276493.

Programs

Magma

[2^n+2*n-3: n in [1..200] | IsPrime(2^n-1) and IsPrime(2^n+2*n-3)];

Maple

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

Extensions

Name suggested by Michel Marcus, Sep 07 2016